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When coin 1 is flipped, it lands on heads with probability   3/5  ; when coin 2...

When coin 1 is flipped, it lands on heads with probability  
3/5  ; when coin 2 is flipped it lands on heads with probability  4/5 .
(a) If coin 1 is flipped 12 times, find the probability that it lands on heads at least 10 times.
(b) If one of the coins is randomly selected and flipped 10 times, what is the probability that it lands on heads exactly 7 times?
(c) In part (b), given that the first of these 10 flips lands on heads, find the conditional probability that exactly 7 of the 10 flips land on heads.
Math   Statistics-And-Probability   
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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. Then

b)

If one of the coins is randomly selected and flipped 10 times, what is the probability that it lands on heads exactly 7 times?

c)

In part (b), given that the first of these 10 flips lands on heads, find the conditional probability that exactly 7 of the 10 flips land on heads.

a) If coin 1 is flipped 12 times, find the probability that it lands on heads at least 10 times.

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