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# Probability

### Probability is explained.

Two events, A and B are equally likely. The chance that either A or B happens on a given trial of an experiment is 0.70, while the chance that they both happen on a given trial is only 0.40. What is the probability that event A happens?

### Normal and Poisson approximation to binomial distribution

In each month, the proportion of "Prize" bonds that win a prize is 1 in 11000. There is a large number of prizes and all bonds are equally likely to win each prize. Show that, for a given month, the probability that a bondholder with 5000 bonds wins at least one prize is 0.365. For a given month find: 1) The probability taht

### Normal & Poisson approximation to binomial distribution

A fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A. By using a suitable approximation to the binomial distribution, calculate the probability of A. The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B. By usin

### Normal approximation to binomial distribution

It is known that in a sack of mixed bean seeds, 35% are yellow beans. Use the normal approximation to the binomial distribution to find the probability that in a sample of 400 beans there are a) less than 120 yellow beans b) between 120 and 150 yellow beans (inclusive) c) more than 160 yellow beans

### Normal approximation to binomial distribution

The probability that a patient recovers from a rare blood disease is 0.6. If 100 people are known to have contracted this disease, what is the probability that less than 50 people recovers from this rare blood disease?

### Binomial Distribution of a Hockey Team

A hockey team consists of 11 players. It may be assumed that, on every occasion, the probability of any one of the regular members of the team being unavailable for selection is 0.15, independently of all other members. Calculate, giving three significant figures in your answers, the probability that, on a particular occasion,

### Poisson approximation to binomial distribution

In a large town, one person in 80, on the average, has blood of type X. a)If 200 blood donors are taken at random, find an approximation to the probability that they include at least five persons having blood of type X. b)How many donors must be taken at random in order that the probability of including at least one donor

### Poisson approximation to binomial distribution

A factory packs bolts in boxes of 500. The probability that a bolt is defective is 0.002. Find the probability that a box contains 2 defective bolts.

### Probability and Cumulative Distribution Function

1. A random variable X has the following cumulative distribution function F(x) = { 1 - e^(-(x+1)) -1</ x < oo 0 elsewhere. a) 25% of the time, X exceeds what value? b) Find the moment generating function of X, or Mx(t) c) Using your result in (b

### Chances of Receiving a Direct Hit by a Scud Missile

Problem: Chances of recieving a direct hit by a scud missile. A scud carries 113kg of explosive, has blast are of 91m in diameter and that missiles are being lobbed into an area 80km long and 48km wide. Assume that missiles fall randomly on this area. a) What is the probability of being in the blast area of a missile? b)

### Step-by-step answer to Poisson Distribution

Let X be a random variable which follows Poisson Distribution. Assume that the probability P(X=1)=P(X=2), find P(X=3).

### Probability

The distribution of blood types for a population are: 40% typeA 9% type B 49% type O 2% type AB Suppose that the blood types are independent and that both the husband and the wife follow this distribution of blood type. a) If the wife has type B, what is the probability that the husband has type B? b) What is the pr

### Probability of Brain Cancer Claims

Brain cancer is a rare disease. In any year there are about 3.1 cases per 100000 od population. Suppose a small medical insurance company has 150000 people on its books. How many claims stemming from brain cancer should the company expect in any year? What is the probability of getting more than 6 claims related to brain c

### Probability Random Variable Constants

Suppose that X is a random variable which can possibly choose 1,2,3,4 with probability P(X=i)=ci, where c is a constant. Find c

### Probability

Samples of size 49 are drawn from a population with a mean of 36 and a standard deviation of 15. What is the probability that the sample mean is less than 33?

### Poisson vs. Gaussian distribution

Radiation: The atoms of a radioactive element are randomly disintegrating and emitting alpha particles. The number of alpha particles emitted per second from these atoms during a 30 second period is recorded as follows. 9.38 8.08 8.36 10.44 9.44 8.05 17.78 7.56 14.17 6.73 9.81 4.79 11.98 9.48 6.32 14.

### Probability Function Expected Amount

A standard die has its faces painted different colors. Faces3,4,6 are red, faces 2 and 5 are black and face 1 is white. a) Find the probability that when the die is rolled, a black or even numbered face shows uppermost. a game is played by rolling the die onvce. If any of the red faces show uppermost, the player wins the

### Random Variables - Joint density

Let X and Y have the joint pdf f x,y(X,Y) = 2e^(-(x+y)) , 0<x<y , 0<y Find P(Y<3X)

### Distribution Dependent Trial

If there are repeated dependent trial, what distribution should be used? a. binomial b. multinomial c. Poisson d. hypergeometric

### At a school, the children miss school 17% of the days.

At a school, the children miss school 17% of the days. If one classroom has 12 children, what is the probability that no children will be absent on a given day. a. .107 b. .17 c. .201 d. .001

### Probability Retail Sales Workers

A retail sales worker finds that the probability of making a sale is .23. If she talks to four customer today, what is the probability of her making four sales? a. 0.003 b. 0.03 c. 0.30 d. 0.001

### Probability of Defective Shipment

A shipment of 50 VCRs had 6 defectives. If a person bought two cameras, find the probability of getting 2 defectives. a. .50 b. .10 c. .0122 d. .05

### Probability of drawing a jack

Find the probability of drawing a jack from an ordinary card deck.

### Mathematical statistics and data analysis

Probability distribution and functions

### Statistics - Probability Consumer Tastes

1) A record store owner wants to determine consumer tastes. She decides to observe customers in her store on a particular day and record the number of minutes the each spends in the Alternative Music and Rap sections of the store. She came up with the following data: Alternative Music Rap Mean = x = 25 Mean = 20 St

### Mean, Standard Deviation & Probability Distribution

Find the mean, standard deviation and probability distribution for the given problems. 1. The average profit per unit for Product A is \$5.32, Product B is \$7.98, and Product C is \$9.69. If the percentages of each sold are 36, 29, and 35 respectively, what is the weighted mean profit per unit? 2. A fleet of cabs fo

### Probability and Expected Value

Find the expected profit in the given question. The Wilhelms Cola Company plans to market a new pineapple-flavored cola this summer. The decision is whether to package the cola in returnable or in no-return bottles. Currently, the state legislature is considering eliminating no-return bottles. Tybo Wilhelms, president of Wilh

### Probability of Guessing Correctly

1. A committee consists of five Chicanos, two Asians, three African Americans, and two Caucasions. a) A subcommittee of four is chosen at random. What is the probability that all the ethnic groups are represented on the subcommittee? b) Answer the question for part (a) if a subcommittee of five is chosen. 2. The game of Ma

### Probability Distinct Size

There are 5 pairs of shoes with distinct size. Now choose any 4 from it randomly, find the probability that they form at least a pair.

### Statistics - polling

1. On February 8, 2002, the Gallup Organization released the results of a poll concerning American attitudes toward the 19th Winter Olympics in Salt Lake City, Utah. The poll results were based on telephone interviews with a randomly selected national sample of 1011 adults, 18 years and older, conducted February 4 - 6, 2002.
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