Television Ratings According to a ratings survey, 40 % of the households in a certain city tune in to the local evening TV news. If ten households are visited at random, what is the probability that four of them will have their television tuned to the local news?

To find:

The probability that four out of ten households will have their television tuned to the local news.

Given:

40% of the households tune in to local evening TV news.

Approach:

For a binomial experiment with two outcomes with outcome of success in each trial equal to p.

The probability of r successes in n trials is equal to

P (r successes in n trials) =C(n,r)pr(1−p)n−r (1)

Calculation:

Interpret this problem as a binomial experiment with two outcomes: a household is tuned to the evening TV news or it is not tuned to the evening TV news. “Success” is the event that a household is tuned to evening TV news.

Probability of success,

p=0.40

Number of trials, n=10

Problem asks probability of four of the households being tuned to the local news. This gives

r=4

Substitute: n,p,r in equation (1) to get