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

Please hit thumps up if the answer helped you

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