The television show 50 Minutes 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 50 Minutes. An advertiser wants to verify that $23 \%$ 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 50 Minutes broadcast.
the probability that at least one household is tuned to 50 Minutes.
$P($ at least one $)=$

Step 1 ：The television show 50 Minutes 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 50 Minutes. An advertiser wants to verify that 23% 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 50 Minutes broadcast.

Step 2 ：We want to find the probability that at least one household is tuned to 50 Minutes.

Step 3 ：The probability of at least one event happening is equal to 1 minus the probability of none of the events happening. In this case, the probability of at least one household tuning into 50 Minutes is equal to 1 minus the probability of none of the 11 households tuning into 50 Minutes.

Step 4 ：The probability of a household not tuning into 50 Minutes is \(1 - 0.23 = 0.77\).

Step 5 ：Since there are 11 households, the probability of none of them tuning into 50 Minutes is \(0.77^{11}\).

Step 6 ：Calculate the probability of none of them tuning into 50 Minutes, which is approximately 0.056.

Step 7 ：Subtract this probability from 1 to find the probability of at least one household tuning into 50 Minutes, which is approximately \(1 - 0.056 = 0.944\).

Step 8 ：Final Answer: The probability that at least one household is tuned to 50 Minutes is approximately \(\boxed{0.944}\).