Two coins are to be flipped The first coin is not balanced i

Two coins are to be flipped. The first coin is not balanced, instead it will land on heads with probability 0.8, the second coin is not either, it will land on heads with probability 0.5. Assuming the flips are independent of each other, and let X = the total number of heads that results.

What is P[X = 1]?

Solution

There are two ways that X = 1.

1. The first one is heads, the second is tails.
2. The first one is tails, the second is heads.

Thus,

P(x = 1) = P(H1) P(T2) + P(T1) P(H2) = 0.8*(1-0.5) + (1-0.8)*0.5 = 0.5 [ANSWER]

**************

Please check the probability of heads for the second coin. It says that it is not balanced, but its probability is 0.5, which is balanced. If this is an error, please resubmit this question as a different question. Thanks!