Question

There are two coins and one of them will be chosen randomly and flipped 10 times. When coin 1 is flipped, the probability that it will land on heads is 0.50. When coin 2 is flipped, the probability that it will land on heads is 0.75. What is the probability that the coin lands on tails on exactly 4 of the 10 flips? Round the answer to four decimal places.

Answer 1

There are two cases to find the probability

Case 1: Coin 1 is chosen

This is a binomial distribution question with
n = 10
p = 0.5 (getting a tail)
q = 1 - p = 0.5
where

Case 2: Coin 2 is chossen
This is a binomial distribution question with
n = 10
p = 0.25
q = 1 - p = 0.75

P(required) = 0.5*P(Case1) + 0.5*P(Case2)
P(required) = 0.5 * 0.2051 + 0.5 * 0.146
P(required) = 0.5 * (0.3511)
P(required) = 0.17555
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