Question

The television show Green's Anatomy has been successful for many years. That show recently had a share of 25 , meaning that among the TV sets in use, 25% were tuned to Green's Anatomy. Assume that an advertiser wants to verify that 25% share value by conducting its own survey, and a pilot survey begins with 15 households have TV sets in use at the time of a Green's Anatomy broadcast.

Find the probability that none of the households are tuned to Green's Anatomy.

Answer 1

The probability that none of the surveyed households are watching Green's Anatomy is approximately 1.33%, which is found by raising the probability of not watching the show (0.75) to the power of the number of households (15).

Step-by-step explanation:

The probability that none of the 15 households surveyed are watching Green's Anatomy, given a 25% share value, can be calculated using the binomial probability formula for the case of 0 households watching. This scenario assumes that each household represents an independent trial with only two possible outcomes (watching or not watching Green's Anatomy).

The probability P of zero households watching the show is given by:

P(X = 0) = (1 - 0.25)^15

Where:

• X is the random variable representing the number of households watching the show.
• 0.25 is the probability of a household watching the show.
• 15 is the total number of households surveyed.

Using this binomial probability formula: P(X = 0) = 0.75^15 P(X = 0) ≈ 0.0133

Therefore, there is approximately a 1.33% chance that none of the 15 households are tuned to Green's Anatomy.