Question

The television show Ghost Whistler has been successful for many years. That show recently had a share of 23, which means, that among the TV sets in use, 23% were tuned to Ghost Whistler. An advertiser wants to verify that 23% share value by conducting its own survey, and a pilot survey begins with 13 households have TV sets in use at the time of a Ghost Whistler broadcast.

Find the probability that none of the households are tuned to Ghost Whistler.
P(none) =

Find the probability that at least one household is tuned to Ghost Whistler.
P(at least one) =

Find the probability that at most one household is tuned to Ghost Whistler.
P(at most one) =

If at most one household is tuned to Ghost Whistler, does it appear that the 23% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Ghost Whistler unusual?)

yes, it is wrong
no, it is not wrong

Answer 1

this is binary, like the other problem ... t = tuned in ... n = not tuned in
... p(t) = .23 ... p(n) = .77

(n + t)^13 = n^13 + 13 n^12 t + ... + 13 n t^12 + t^13

P(none) = n^13 = .77^13

P(at least one) means not none ... P(at least one) = 1 - P(none)

P(at most one) means one or none ... the sum of the 1st two terms
... (.77^13) + (13 * .77^12 * .23)