Final answer:
The probability that both John and Jane watch a certain television show is 0.32, or 32%, calculated using the conditional probability formula P(J AND K) = P(K) × P(J|K) with the given probabilities.
Step-by-step explanation:
John and Jane are married, and we want to find the probability that both watch a certain television show. Let's define P(J) as the probability that John watches the show and P(K) as the probability that Jane watches the show. The question provides us with the following probabilities: P(J) = 0.50, P(K) = 0.40, and the conditional probability that John watches the show given Jane does, P(J|K), is 0.80.
To find the probability that both John and Jane watch the show, we use the formula for conditional probability:
P(J AND K) = P(K) × P(J|K)
Substituting the given values in:
P(J AND K) = 0.40 × 0.80
P(J AND K) = 0.32
Therefore, the probability that both John and Jane watch the show is 0.32, or 32%.