Question

Suppose that in a large metropolitan area, 85% of all households have cable tv. Suppose you are interested in selecting a group of six households from this area. Let X be the number of households in a group of six households from this area that have cable tv. For what proportion of groups will exactly four of the six households have cable tv?

Answer 1

Solution :

Let X denotes the number of the households tha have a cable TV.

Percentage of household that have a cable TV = 85 %

$X \sim \text{Binomial}(6, 0.85)$

Here, we can see that each of the observations is independent and the number of the observations is fixed, n.

The probability of the success P is the same for each of the outcomes.

Therefore,

$P(X=4)= \binom{6}{4}0.85^40.15^2$

               = 0.08324