Exam 2 MAT 1201 Summer 2014 (16) 1. I roll two dice one time and look at the result, let the events be defined as follows Event A = die 1 is a 4 event B = sum of the dice is 9 event C = die 2 is even a) Are events A and B independent, dependent or mutually exclusive? Why or why not? b) Are events A and C independent, dependent or mutually exclusive? Why or why not? c) Are events B and C independent, dependent or mutually exclusive? Why or why not d) Give an example of any Event D, that can only involve one die, that is mutually exclusive of event B (9) 2. I have two dice and one is loaded so that the roll of 3 occurs 40% of the time and the other rolls come up equally so P(3) = .4 P(1) = P(2) = P(4) = P(5) = P(6) = .12 The second die is fair a) Find the probability of rolling a sum of 5 on these dice b) Find the probability of rolling 3 straight sums of 5 on these dice c) If the second die was a 2 find the probability of rolling a sum of 5 on these dice? (9) 3. If P(A) = .3 and P(A/B) = .5 and P(A B) = .05 find the following' a) P(B) b) P(A /B) c) P(A U B) (4) 4. What is the probability of rolling exactly one sum of 10 in 3 rolls of the dice? (4) 5. Taylor Swift and Kanye West are playing a dice rolling game. Kanye has rolled 3 straight sums of 7 and then states he is betting against rolling a 7 on the next roll because it is less likely to occur. He reasons that the probability of getting 4 straight sums of 7 is (1/6)(1/6)(1/6)(1/6) = 1/1296 so 7 is less likely to occur on the 4th roll. At this point Taylor states to the people in the crowd that Kanye is an idiot and the probability is still 1/6 of him getting a 7 on the next roll and he should learn statistics. Who is right and why? (4) 6. If events A and B are independent what would P(B/A ) simplify to? (4) 7. Find the probability of rolling a sum of 7 in 2 rolls of the dice? (you stop as soon as you roll a 7) (5) 8. You are drawing cards from a standard 52 card deck. If you draw out a diamond you win $10. If you draw out any other card you lose. So I want you to tell me the dollar amount to lose in order for this to be a break even game (4) 9. You are about to play a best 4 out 7 games of black jack against your brother (the series stops as soon as one player wins 4 games). Assume you each have a 50% chance of winning each game and the games are independent of one another. What is the probability there will be "sweep" in the series meaning either one of you wins the contest in just 4 games without a 5th or 6th or 7th game being necessary? (10) 10. I roll two dice one time. Let event A = sum of the dice is 9, event B = sum of the dice is odd and let event C = die 1 is even, find the following probabilities a) P(A/B) b) P(B/A) c) P(C/B) d) P(C/A) e) P(C /A) (10) 11. The following table gives a child's gender and favorite subject at school math english gym Lunch Boy 20 20 60 40 girl 30 40 40 50 One child is selected at random find the following probabilities: a) The child selected has math as a favorite subject and is a boy? Answer: _____________ b) The child is a boy given they like gym as their favorite subject? Answer: ________ c) The child selected is a boy or they like lunch as the favorite subject? Answer: _______ d) The child selected is boy or a girl? Answer: _______________ e) Are the events girl and lunch independent, dependent or mutually exclusive? Answer: _______________ (4) 12. Find the probability of getting at least one sum of 9 in 14 rolls of the dice? (4) 13. Explain in words what it means for two events to be mutually exclusive (9) 14. If P(A) = .36, P(B) = .32 and P(A B) = .21 find the following a) P(A U B) b) P(B/A) c) P(A/B) (8) 15. In a lottery game there are 40 numbers of which you have to match 6 of the numbers and also you must match one ball from a separate drum of 19 balls. a) Find the probability you win this game by matching the 6 out of 40 and then the one from the 19 b) If it costs $2 for a lottery ticket and the payout for winning is $100,000,000 find your expected earnings in this game and INTERPRET the answer