The television show Ghost Whistler has been successful for many years. That show recently had a share of 29 , which means, that among the TV sets in use, 29% were tuned to Ghost Whistler. An advertiser wants to verify that 29% 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.
Answer
Final Answer: The probability that none of the households are tuned to Ghost Whistler is approximately \(\boxed{0.023}\).
Step 1 ：The problem is asking for the probability that none of the households are tuned to Ghost Whistler. This is a binomial distribution problem where the number of trials is the number of households (n=11) and the probability of success (a household is tuned to Ghost Whistler) is the share value (p=0.29).
Step 2 ：The formula for the probability mass function of a binomial distribution is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(C(n, k)\) is the binomial coefficient, p is the probability of success, and n is the number of trials.
Step 3 ：In this case, we want to find \(P(X=0)\), so k=0.
Step 4 ：Substituting the given values into the formula, we get \(P(X=0) = C(11, 0) * (0.29^0) * ((1-0.29)^(11-0))\).
Step 5 ：Solving the above expression, we get a probability of approximately 0.023.
Step 6 ：Final Answer: The probability that none of the households are tuned to Ghost Whistler is approximately \(\boxed{0.023}\).
