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# Pre-Cal 40S May 28, 2009

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Independent and Dependent probabilities.

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### Pre-Cal 40S May 28, 2009

1. 1. All About Red & Blue Marbles or Independent and Dependent Probability Biglie by ﬂickr user mat.teo
2. 2. A coin is ﬂipped three times. Draw a tree diagram to illustrate the sample space.
3. 3. A fair six-sided die is rolled twice. Draw a chart to illustrate the sample space.
4. 4. A fair six-sided die is rolled twice. Draw a chart to illustrate the sample space.
5. 5. A bus is scheduled to arrive at a train station at any time between 07:05 and 07:15 inclusive. A train is scheduled to arrive between 07:11 and 07:17 inclusive. The arrival of a bus at 7:06 and a train at 07:14 can be represented by the ordered pair (6, 14). Times are expressed in whole minutes. a) Sketch a sample space for this event (use a chart). b) How many ordered pairs are there in this sample space? c) How many ordered pairs have the bus and the train arriving at the same time? d) How many ordered pairs have the train arriving after the bus? e) What is the probability of the bus arriving after the train?
6. 6. A marble is drawn, replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?
7. 7. A marble is drawn, replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?
8. 8. Independent Events Events in which the outcome of one event does not affect the outcome of the other event. Dependent and independent probabilities ... A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and then REPLACED back in the bag. A second marble is selected, what is the probability that it is blue?
9. 9. A marble is drawn, not replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?
10. 10. A marble is drawn, not replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?
11. 11. A marble is drawn, not replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?
12. 12. Dependent Events If the outcome of one event affects the outcome of another event, then the events are said to be dependent events. Dependent and independent probabilities ... A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and NOT REPLACED back in the bag. A second marble is selected, what is the probability that it is blue?
13. 13. Identify each of the following as experiments involving dependent in independent events. Drag and Drop Baby! INDEPENDENT DEPENDENT (a) Toss a coin and roll a die six. INDEPENDENT (b) Draw 2 cards from a 52 card deck, without replacement. DEPENDENT (c) Draw 2 cards from a 52 card deck, with replacement. INDEPENDENT
14. 14. In a family of 3 children, with boys and girls equally likely to be born, what is the probability that exactly 2 kids are girls?
15. 15. Two marbles are drawn. If the 1st marble is blue it is discarded and replaced with a red. Similarly, if the 1st marble is red it is discarded and replaced with a blue one. What is the probability that the second marble is blue?
16. 16. Two marbles are drawn. If the 1st marble is blue it is discarded and replaced with a red. Similarly, if the 1st marble is red it is discarded and replaced with a blue one. What is the probability that the second marble is blue?
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