Question

Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses. Have Shopped Have Never Shopped Male 500 700 Female 300 500 If one adult is selected at random from these 2000 adults, find the probability that this adult has never shopped on the Internet is a male has shopped on the Internet given that this adult is a female is a male

Answer 1

The probability that an adult has never shopped on the Internet given that this adult is a male has shopped on the Internet and that this adult is a female is a male is 0.

Step-by-step explanation:

To find the probability that an adult has never shopped on the Internet given that this adult is a male has shopped on the Internet and that this adult is a female is a male, we need to use conditional probability.

The probability of a male adult having shopped on the Internet is 500/2000 = 0.25.

The probability of an adult being a female is a male is 300/2000 = 0.15.

Therefore, the probability that an adult has never shopped on the Internet given that this adult is a male has shopped on the Internet and that this adult is a female is a male can be calculated using Bayes' theorem:

P(Never shopped | Male shopped and Female is a male) = P(Never shopped and Male shopped and Female is a male) / P(Male shopped and Female is a male)

Using the given table, P(Never shopped and Male shopped and Female is a male) = 0.

P(Male shopped and Female is a male) = P(Male shopped) * P(Female is a male) = 0.25 * 0.15 = 0.0375.

Therefore, P(Never shopped | Male shopped and Female is a male) = 0/0.0375 = 0.