Math 10B Quiz 4-
1. Bob is participating in a basketball competition on Monday and he has to decide whether or not to run a marathon on Sunday. He knows that if he runs the marathon, the probability he wins at basketball is 0.1, whereas if he doesn't run the marathon, the probability he wins at basketball is 0.5. On Sunday, he flips a fair coin to decide whether or not to run the marathon.
What is the probability that he ran the marathon, given that he won at basketball?
2. A fair coin is tossed 7 times. Let A be the event that tosses 1, 2, 3 come up heads, B the event that tosses 3, 4, 5 come up heads and C the event that tosses 5, 6, 7 come up heads.
(a) Are the events A and C independent?
(b) Are the events A, B, and C independent?
3. A fair coin is tossed 7 times. Let X be the random variable counting the number of heads. Compute the probability that X ≥ 3. Give your answer in the form a/b where a and b are integers.