Questions: The probability of a company having a section in the newspaper is 0.43, and the probability of a company having a website given that the company has a section in the newspaper is 0.84. What is the probability of a company having a website and a section in the newspaper? Round your answer to three decimal places.

Solution Steps

To find the probability of a company having both a section in the newspaper and a website, we can use the concept of conditional probability. Specifically, we use the formula for the joint probability of two events: \( P(A \cap B) = P(B|A) \times P(A) \), where \( P(A) \) is the probability of having a section in the newspaper, and \( P(B|A) \) is the probability of having a website given that the company has a section in the newspaper.

Let \( P(A) \) be the probability of a company having a section in the newspaper, which is given as: \[ P(A) = 0.43 \] Let \( P(B|A) \) be the probability of a company having a website given that it has a section in the newspaper, which is given as: \[ P(B|A) = 0.84 \]

To find the probability of a company having both a section in the newspaper and a website, we use the formula for joint probability: \[ P(A \cap B) = P(B|A) \times P(A) \] Substituting the known values: \[ P(A \cap B) = 0.84 \times 0.43 \]

Calculating the above expression gives: \[ P(A \cap B) = 0.3612 \] Rounding this to three decimal places, we have: \[ P(A \cap B) \approx 0.361 \]

Final Answer