Question

the probability that coin a and coin b come up with head are 0.3 and 0.5, respectively. alice repeats the following process: she flips one coin until a tail comes up. the coin is put aside and she starts to flip another coin. (a) find the portion of flips that coin a is used. (b) if alice starts with coin a, find the probability that coin b is used on the 5th flip? (please express your answer up to 4 decimal places) 2

Answer 1

The portion of flips that coin A is used is 0.7. If Alice starts with coin A, the probability that coin B is used on the 5th flip is 0.5.

Step-by-step explanation:

To find the portion of flips that coin A is used, we need to consider the probability of getting tails on coin A. The probability of getting tails on coin A is 1 - 0.3 = 0.7.

Since Alice continues flipping a coin until a tail comes up, the portion of flips that coin A is used is equal to the probability of getting tails on coin A, which is 0.7.

To find the probability that coin B is used on the 5th flip if Alice starts with coin A, we need to consider the probability of getting tails on coin A on the first 4 flips.

The probability of getting tails on coin A on each flip is 0.7.

So, the probability of getting tails on coin A on the first 4 flips is (0.7)^4.

Since Alice starts with coin A, the probability that coin B is used on the 5th flip is the probability of getting heads on coin B, which is 0.5.