A TV executive is interested in the popularity of a particular cable TV show. She has been told that a whopping 65% of American households would be interested in tuning in to a new network version of the show. If this is correct, what is the probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show? Assume that the 6 households constitute a random sample of American households.

Question

A TV executive is interested in the popularity of a particular cable TV show. She has been told that a whopping 65%  of American households would be interested in tuning in to a new network version of the show. If this is correct, what is the probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show? Assume that the 6  households constitute a random sample of American households.

kropot72 · Answer

The probabilityof each of the 6 households being monitored would be interested in the new show is 0.65. The decision of each household is independent of the others' decisions, therefore the probability multiplication theorem applies.
$$P(6Households)=0.65\times 0.65\times 0.65\times 0.65\times 0.65\times 0.65=?$$