Question

The television show Lett3rs has been successful for many years. That show recently had a share of 16, which means, that among the TV sets in use, 16% were tuned to Lett3rs. An advertiser wants to verify that 16% share value by conducting its own survey, and a pilot survey begins with 14 households have TV sets in use at the time of a Lett3rs broadcast.Find the probability that none of the households are tuned to Lett3rs.P(none) = Find the probability that at least one household is tuned to Lett3rs.P(at least one) = Find the probability that at most one household is tuned to Lett3rs.P(at most one) =

Answer 1

In this scenario, there are only two outcomes. It is either the household is tuned to Lett3rs or not. The outcomes are independent. This means that we can apply the binomial probability. the formula is expressed as

P(x) = nCx * p^x * q^(n - x)

where

n = number of trials

x = number of succeses

p = probability of success

q = probability of failure

From the information given,

n = 14

p = 16% = 16/100 = 0.16

q = 1 - 0.16 = 0.84

1) P(none) = P(x = 0)

Thus,

P(none) = 14C0 * 0.16^0 * 0.84^(14 - 0)

P(none) = 0.087

2) P(at least one) = P(x ≥ 1) = 1 - P(x = 0)

P(at least one) = 1 - 0.087

P(at least one) = 0.913

P(at most one) = P(x = 0) + P(x = 1)

P(x = 1) = 14C1 * 0.16^1 * 0.84^(14 - 1) = 0.2322

P(at most one) = 0.087 + 0.2322

P(at most one) = 0.32