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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The probability that event M will not occur is 0.8 and the probability

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Math Expert V
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The probability that event M will not occur is 0.8 and the probability  [#permalink]

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The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

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The probability that event M will not occur is 0.8 and the probability  [#permalink]

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Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

We are given that the probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6 and that events M and R cannot both occur.

We need to determine the probability that either event M or event R will occur.

The probability that event M will occur is 1 - 0.8 = 0.2 = 1/5

The probability that event R will occur is 1 - 0.6 = 0.4 = 2/5

Since events M and R cannot both occur , the probability that either event M or event R will occur is 1/5 + 2/5 =3/5.

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Manager Joined: 18 Jan 2010
Posts: 238
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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8
5
Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

P(R) = 1 - 0.8= 0.2
P(M) = 1 -0.6 = 0.4

Given that both events are mutually exclusive.

Prob that either event M or event R will occur = 0.2+0.4 = 0.6 = (6/10) = (3/5)

##### General Discussion
Director G
Joined: 20 Feb 2015
Posts: 734
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The probability that event M will not occur is 0.8 and the probability  [#permalink]

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1
p(m) =0.2
p(r) =0.4
p(m intersection r) = 0 (If events M and R cannot both occur)
p(m or r) = 0.2+0.4 =0.6

Corrected !!

Originally posted by CounterSniper on 15 Jun 2016, 03:52.
Last edited by CounterSniper on 15 Jun 2016, 04:31, edited 1 time in total.
Intern Joined: 01 May 2015
Posts: 36
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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1
Got it wrong.

p(m) =0.2
p(r) =0.4

So, I calculated probability as sum of:

i) m occurs but r does not occur = 0.2*0.6
ii) r occurs but m does not occur = 0.4*0.8

So, probability = 0.2*0.6 + 0.4*0.8 = 0.44 = 11/25!
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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5
4
Just made a mistake by multiplying 0.2 and 0.4, got $$\frac{2}{25}$$

Note to self: "multiply" when there is an "AND", and "add" when there is an "OR"

we should be adding 0.2+0.4 = 0.6 or $$\frac{3}{5}$$
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Intern B
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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1
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25 Manager S
Joined: 13 Apr 2010
Posts: 86
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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5
3
shonakshi wrote:
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25 I think , you are trying to calculate probability by multiplying P(M)*P(~R) + P(R)*P(~M) . This is wrong .
Formula is P(M or R) = P(M) + P(R) - P (M and R) => 0.2 + 0.4 - 0 = > 0.6 or 3/5 (Answer is C) .
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The probability that event M will not occur is 0.8 and the probability  [#permalink]

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4
shonakshi wrote:
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25 https://people.richland.edu/james/lectu ... 5-rul.html

Hope that helps..
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Intern B
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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ScottTargetTestPrep wrote:
Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

We are given that the probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6 and that events M and R cannot both occur.

We need to determine the probability that either event M or event R will occur.

The probability that event M will occur is 1 - 0.8 = 0.2 = 1/5

The probability that event R will occur is 1 - 0.6 = 0.4 = 2/5

Since events M and R cannot both occur , the probability that either event M or event R will occur is 1/5 + 2/5 =3/5.

We should take into consideration that both cannot occurs. please explain
Board of Directors D
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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1
2
Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6.If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

M' = 0.80 So M = 0.20
R' = 0.60 So R = 0.40
Quote:
probability that either event M or event R will occur?

M+R = M + R - MR
Quote:
events M and R cannot both occur

So , MR = 0

M+R = 0.20 + 0.40 - 0

Or, M+R = 0.60

Hence answer will be 0.60 or (C) 3/5

SOHAM6185 wrote:
We should take into consideration that both cannot occurs. please explain

The reason is highlighted...

Try to solve this question using VENN Diagram approach it will be crystal clear...
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Director P
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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sb0541 wrote:
shonakshi wrote:
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25 I think , you are trying to calculate probability by multiplying P(M)*P(~R) + P(R)*P(~M) . This is wrong .
Formula is P(M or R) = P(M) + P(R) - P (M and R) => 0.2 + 0.4 - 0 = > 0.6 or 3/5 (Answer is C) .

yes, that is why p(m and n) need to be zero.
Manager G
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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1
shonakshi wrote:
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25 The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

Let's break this down

M will not occur = 0.8; M will occur = 0.2
R will not occur = 0.6; R will occur = 0.4

P(M or R) = P(M) + P(R) - P (M and R)
P(M or R) = 0.2 + 0.4 - 0
P(M or R) = 0.6 = 6/10 = 3/5

Note: Multiplying occurrence that will not occur + Multiplying occurrence that will occur is not equal to either event M or event R will occur
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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shonakshi wrote:
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25 Once you say that event M and event R can not occur together , it means that both are mutually exclusive.
P(M).P(R)=0

Posted from my mobile device

Posted from my mobile device
Director P
Joined: 29 Jun 2017
Posts: 954
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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be careful
there are 2 cases
case 1
1= p (a happen)+ p (b happen)- p (both a and b happen) +p (neither a nor b happen) . this is ven digram

case 2
1= p (a dose not happen)+ p(b dose not happen)- p (neither a nor b happen)+ p (both a and b happen). this is ven diagram
p ( only a happen) is in p (b dose not happen).

so, there is two scenario here.
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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GMATSkilled wrote:
shonakshi wrote:
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25 The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

Let's break this down

M will not occur = 0.8; M will occur = 0.2
R will not occur = 0.6; R will occur = 0.4

P(M or R) = P(M) + P(R) - P (M and R)
P(M or R) = 0.2 + 0.4 - 0
P(M or R) = 0.6 = 6/10 = 3/5

Note: Multiplying occurrence that will not occur + Multiplying occurrence that will occur is not equal to either event M or event R will occur

How can that formula be correct? What if the problem had said the probability that M will not occur is .5, and the probability that R will not occur is .5. Then according to your formula, you'd have:
P(M or R) = P(M) + P(R) - P(M and R)
P(M or R) = .5 + .5 - 0
P(M or R) = 1

So if two mutually exclusive events each have a 1/2 probability of occurring, then the probability of at least one of them occurring is 1 (100% of the time?) That doesn't make any sense to me, so I'm not exactly sure why that formula is what you're supposed to apply.

In a real-life scenario, that's like saying the Cardinals have a 40% chance to win the World Series, and the Yankees have a 20% chance to win, so the chance that one of them wins is 60% (since both of them cannot win)... Which doesn't make any sense. Again, what if you said the cardinals have an 80% chance to win and the Yankees have a 30% chance to win. So the chance that one of them wins is 110%?

The language in the question doesn't seem to suggest that either M or N must occur... In order to interpret the question the way the answer seems to, I would think the language would have to say something like "Out of 100 trials, M did not occur 80% of the time and N did not occur 60% of the time; if N and M never occurred on the same trial, what's the probability that a randomly selected trial will have M OR N occurring?" In that case, when you already have a list of events that happened, you could apply the formula P(M or R) = P(M) + P(R) - P(M and R)... Take it back to the 50% example, if you know that M occurred 50% of the time and N occurred 50% of the time, and M and N cannot happen, then you know that at least M or N had to happen every time. But when you're talking about the probability of a future event, as the problem seems to suggest, it doesn't make sense to just add the probabilities.

Can someone tell me if/how my reasoning is incorrect?
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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Can someone please address the above challenge to this question's answer? I also disagree with the application of the formula used in the solution. This question is posing a future probability event.

What if the question was modified to probability of M occurring=90% and R occurring=90%? (So not occurring for either event is 10%). M and R are still mutually exclusive events.

If we apply the recommended formula P(M or R)=P(M) + P(R) -P(M and R), we get .9+.9-0=1.8. Wait, 1.8!? That doesn't even make sense.
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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bluenux wrote:
Can someone please address the above challenge to this question's answer? I also disagree with the application of the formula used in the solution. This question is posing a future probability event.

What if the question was modified to probability of M occurring=90% and R occurring=90%? (So not occurring for either event is 10%). M and R are still mutually exclusive events.

If we apply the recommended formula P(M or R)=P(M) + P(R) -P(M and R), we get .9+.9-0=1.8. Wait, 1.8!? That doesn't even make sense.

Both can't occur at the same time means they're mutually exclusive events. Only M or R can happen, but not both! Therefore, you don't have to subtract the probabilty for P(M and R)
-> P(M or R) = P(M) + P(R)
-> P(M) = 0.2
-> P(R) = 0.4
-> P(M or R) = 0.2 + 0.4 = 0.6 = 3/5
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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mskx wrote:
bluenux wrote:
Can someone please address the above challenge to this question's answer? I also disagree with the application of the formula used in the solution. This question is posing a future probability event.

What if the question was modified to probability of M occurring=90% and R occurring=90%? (So not occurring for either event is 10%). M and R are still mutually exclusive events.

If we apply the recommended formula P(M or R)=P(M) + P(R) -P(M and R), we get .9+.9-0=1.8. Wait, 1.8!? That doesn't even make sense.

Both can't occur at the same time means they're mutually exclusive events. Only M or R can happen, but not both! Therefore, you don't have to subtract the probabilty for P(M and R)
-> P(M or R) = P(M) + P(R)
-> P(M) = 0.2
-> P(R) = 0.4
-> P(M or R) = 0.2 + 0.4 = 0.6 = 3/5

I recognize that point, which is why my calculation equated 0 for P(M and R). The confusion still stands...
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Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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bluenux wrote:
mskx wrote:
bluenux wrote:
Can someone please address the above challenge to this question's answer? I also disagree with the application of the formula used in the solution. This question is posing a future probability event.

What if the question was modified to probability of M occurring=90% and R occurring=90%? (So not occurring for either event is 10%). M and R are still mutually exclusive events.

If we apply the recommended formula P(M or R)=P(M) + P(R) -P(M and R), we get .9+.9-0=1.8. Wait, 1.8!? That doesn't even make sense.

Both can't occur at the same time means they're mutually exclusive events. Only M or R can happen, but not both! Therefore, you don't have to subtract the probabilty for P(M and R)
-> P(M or R) = P(M) + P(R)
-> P(M) = 0.2
-> P(R) = 0.4
-> P(M or R) = 0.2 + 0.4 = 0.6 = 3/5

I recognize that point, which is why my calculation equated 0 for P(M and R). The confusion still stands...

How to you calculate P(M and R) that you get 0?

and means multiply

P(M or R) = P(M) + P(R) - P(M and R)
P(M or R) = P(0.9) + P(0.9) - P(0.9*0.9) -> 0.9*0.9 is not 0
But please consider that P(M or R) = P(M) + P(R) -P(M and R) is wrong because its a mutually exclusive event. Re: The probability that event M will not occur is 0.8 and the probability   [#permalink] 24 Oct 2018, 12:44

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# The probability that event M will not occur is 0.8 and the probability
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