probability Law and Order

Question

The television show Law & Disorder has been successful for many years. That show recently had a share of 17, meaning that among the TV sets in use, 17% were tuned to Law & Disorder. Assume that an advertiser wants to verify that 17% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a Law & Disorder broadcast. Show your work.

Find the probability that none of the households are tuned to Law & Disorder.

Find the probability that at least one household is tuned to Law & Disorder.

P(at least one)

Find the probability that at most one household is tuned to Law & Disorder.

P(at most one) 

If at most one household is tuned to Law & Disorder, does it appear that the 17% share value is wrong?

Answer 1

n = sample size p = probability tuned to L&O x = number of households tuned to L&O

For these problems n=10 and p = 0.7.

Use binomial probability formula to find probability x number of sets tuned to L&O::

C(n,x) p^x (1-p)^(1-x) where C is the number of combinations of n households taken x at a time.

Find the probability that none of the households are tuned to Law & Disorder.

set x to 0 in formula and compute

Find the probability that at least one household is tuned to Law & Disorder.

P(at least one)

that will be equal to 1 - the probability that none of the households are tuned to L&O

Find the probability that at most one household is tuned to Law & Disorder.

P(at most one) 

set x to 1 in formula and compute then add that to probability computed for x = 0 in first problem.

If at most one household is tuned to Law & Disorder, does it appear that the 17% share value is wrong?

if probability computed in previous problem differs significantly from 17% then that estimate would be wrong.