Question

A television​ network, Network​ A, is scheduling its fall lineup of shows. For the Tuesday night 8 p.m.​ slot, Network A has selected its top show. If its rival​ network, Network​ B, schedules its top show during the same time​ slot, Network A estimates that it will get 1.1 million viewers.​ However, if Network B schedules a different show during that time​ slot, Network A estimates that it will get 1.6 million viewers. Network A believes that the probability that Network B will air their top show is 0.4 and the probability that Network B will air another show is 0.6.

Determine the expected number of viewers (in millions) for Network​ A's top show.
Network A expects that how many million people will watch their show (type an integer or decimal).

Answer 1

The number of viewers Network A expects will watch their show is 1.4 million viewers.

Explanation:

The expected value is calculated by multiplying the possible outcomes by the probability of their occurrence and adding the results

Therefore, we have the expected value given by the following expression;

Estimated network A viewers where network B schedule top show = 1.1 million viewers

Estimated network A viewers where network B schedule a different show = 1.6 million viewers

Probability that Network B will air its top show = 0.4

Probability that Network B will air another show = 0.6

We therefore have;

Expected value, E of Network A viewers is therefore;

E = 1.1 × 0.4 + 1.6 × 0.6 = 0.44 + 0.96 = 1.4 million viewers.

Network A expects 1.4 million viewers will watch their show.