Question

It is very common for television series to draw a large audience for special events of for cliff-hanging story lines. suppose that on one of these occasions, the special show drew viewers from 38.2% of all us tv households. suppose that three tv households are randomly selected. what is the probability that all three households viewed this special show?

Answer 1

The given case satisfies the condition of Binomial Experiment so we can use the Binomial Probability to answer this question.

Conditions for a Binomial Experiment are:
1) The sample is simple random sample
2) The probability of success is constant
3) The trials are independent
4) There are a fixed number of trials

Probability of success on a single trial = p = 0.382
Number of trials = n = 3
Number of successful trials= x = 3


The formula of the Binomial probability is:
P( 3 out of 3 success) = $3C_{3} p^{3} (1-p)^{3-3}$

Using the values, we get:

P (3 out of 3) = 0.557 = 5.57%

Thus the probability that all three households viewed this special show is 5.57%