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Question

The television show Ghost Whistler has been successful for many years. That show recently had a share of 18, meaning that among the TV sets in use, 18% were tuned to Ghost Whistler. Assume that an advertiser wants to verify that 18% share value by conducting its own survey, and a pilot survey begins with 11 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 18% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Ghost Whistler unusual?)

1. yes, it is wrong
2. no, it is not wrong

Answer 1

If the probability of any set being on Ghost Whistler is 18%, then the probability of it not being tuned in is 82%. The chance of 11 sets all being not tuned in would be (0.82)^11.

At least one set being tuned in includes any count of tuned in sets except zero, which is what we just calculated in the previous question. So the answer here is: 1 - (0.82)^11.

Simliarly "at most one" includes any count except all. If one set being tuned in is 18%, then 11 out of 11 sets being tuned in would be (0.18)^11. At most one set would be 1 - (0.18^11).