Suppose three different fair coins are flipped and exactly two of the coins came up heads. What is the probability that the first coin came up heads?A. 1/3B. 1/2C. 2/3D. None of the above are correct.

12Conditional Probabilities•The probability of Event A conditional on Event B is given by, •This is also described as the probability of A given B.•If are disjoint and . Then the probabilty of any Event Bis,•If two events are independent

Self Clicker Question #24 (1pt.): Suppose two fair coins are tossed. What is the probability that the second coin turned up tails if you know that at least one of the coins is a head.

Self Clicker Question #25 (1pt.): Suppose a class is composed of 60% girls and 40% boys. 30% of the girls have long hair and 20% of the boys have long hair. If a student is randomly chosen from the class, what is the probability the student will have long hair?

15Conditional Probabilities•Bayes Theorem•If there are two events A and B,•If are disjoint and , we can rewrite this as,•In the simple case where ,

Group Clicker Question #26 (1pt.): Suppose a car insurance company can divide drivers into risky and safe drivers. Over the course of a year, a risky driver will have a accident with probability .4 and a safe driver with probability .2. If 30% of the population are risky drivers, what is the probability that a new policyholder will have an accident in the first year?