John and jane are married. the probability that john watches a certain television show is 0.4. the probability that jane watches the show is 0.5. the probability that john watches the show, given that jane does, is 0.2.

(a) find the probability that both john and jane watch the show. (round your answer to 2 decimal places.) probability
(b) find the probability that jane watches the show, given that john does. (round your answer to 3 decimal places.) probability
(c) do john and jane watch the show independently of each other

(a) 0.1

(b) 0.04

(c) NO.

Explanation:

(a) P(Jane and John) = P(John | Jane) × P(Jane)

= (0.2) × (0.5)

= 0.1

(b) P(Jane | John) = P(Jane and John) ÷ P(John)

= (0.1) ÷ (0.4)

= 0.04

(c) P(Jane) × P(John) = (0.5) × (0.4)

                                  = 0.20

P(Jane and John) ≠ P(Jane) × P(John)  

0.1 ≠ 0.20

The two events are not independent do to the fact that P(Jane and John) ≠ P(Jane) × P (John).

With that being said, John and Jane do not watch the show independently of each other.

reducing the scale of the market for a new product.