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The CBS television show 60 Minutes has been successful for many years. At one time 30% of all TV sets were tuned to that show. Assume that an advertiser wants to verify that 30% by conducting its own survey, and a pilot survey begins with 10 household having TV sets in use at the time of a 60 Minutes broadcast. a. Find the probability that none of the households are tuned to 60 Minutes. b. Find the probability that at least one household is tuned to 60 Minutes.

Respuesta :

Answer:

a) The probability that none of the households are tuned to 60 Minutes is 2.8%

b) The probability that at least one household is tuned to 60 Minutes is 97.2%

Step-by-step explanation:

Firstly we have to find the probability that none of the households are tuned to 60 Minutes.

There is a sample of 10 households, where the probabilities of each households being tuned are independent. So, being H1 tuned or not, the probability of H2,H3,... being tuned will each be 30%.

So, each of the 10 households have 70% probability of not being tuned to 60 minutes.

This means that the probability [tex]P_{0}[/tex] of none of 10 households being connected is:

[tex]P_{0} = (0.7)^10[/tex]

[tex]P_{0} = 0.028[/tex]

[tex]P_{0} = 2.8%[/tex]

Now in b), the sum of all the probabilities is 100%. So, the probability that at least one household is tuned to 60 Minutes is 100% subtracted by the probability that none of the households is tuned. So

[tex]P_{1+} = 100 - P_{0}[/tex]

[tex]P_{1+} = 97.2%[/tex]

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