Question

When coin 1 is flipped, it lands on heads with probability .4; when coin 2 is flipped, it lands on heads with probability .7. One of these coins is randomly chosen and flipped 10 times. (a) what is the probability that exactly 7 of the 10 flips lands on heads? (b) Given that the first of these 10 flips lands heads, what is the conditional probability that exactly 7 of these 10 flips lands on heads?

Answer 1

Solution Let E1 be the event that coin 1 is selected and E2 the event that coin 2 is selected. Let F be the event that exactly 7 of the 10 flips lands on heads, let G be the event that the fist flip is heads.