Suppose that a coin is flipped 10 times. Let A be the event that 3 of the first 9 flips are heads, and let B be the event that the 10th flip is heads. What is P(B|A)? How does it compare to P(B)? Solution Not stated here is if it is a fair coin. While we will get a similar answer in both ways, I will go ahead and make this assumption. P(3 of the first 9 flips are heads) = C(9,3)1/29 = 84/512 = 21/128 P(3 of the first 9 flips are heads and the tenth flip is a head) = the number of ways that 3 of the first 9 flips are heads and the tenth flip is a heads/the total number of flips = C(9,3) * 1/210 = 84/1024 = 21/256 Then, P(B|A) = P(the tenth flip = heads and 3 of the first 9 flips are heads)/P(3 of the first 9 are heads) = 21/256/(21/128) = 1/2 P(B) = 1/2 Thus, P(B|A) = P(B).