. 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 obtained.

Have shopped Have never shopped
Male 500 700
Female 300 500
Suppose one adult is selected at random from these 2000 adults. Find the following probabilities
a) P(has never shopped on the Internet and is a male)
b) P(has shopped on the Internet and is a female)

A) 0,35

B) 0,15

0,35

a. 7/12

b. 3/8

To find the probabilities, we need to use the information given in the two-way classification table. Let's first calculate the total number of males and females in the sample:

Total number of males = 500 (have shopped) + 700 (have never shopped) = 1200
Total number of females = 300 (have shopped) + 500 (have never shopped) = 800

a) To find P(has never shopped on the Internet and is a male), we need to divide the number of males who have never shopped (700) by the total number of adults (2000):

P(has never shopped on the Internet and is a male) = 700/2000 = 0.35

b) To find P(has shopped on the Internet and is a female), we need to divide the number of females who have shopped (300) by the total number of adults (2000):

P(has shopped on the Internet and is a female) = 300/2000 = 0.15

Therefore, the probabilities are:
a) P(has never shopped on the Internet and is a male) = 0.35
b) P(has shopped on the Internet and is a female) = 0.15