Question

60 % of the population of a town read either magazine A or magazine B, and 10% read both.

2.1 If 50% read magazine A, what is the probability that one person, selected at random, reads magazine B? [3]

2.2 What type of events are A and B? Give a reason for you answer? [2]

2.3 Draw a venn diagram to illustrate you answer. [3]

Answer 1

Given $P(A\cup B)=0.6, P(A\cap B)=0.1$

2.1

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

Given P(A)=0.5.

Then

$$P(B)=P(A\cup B)+P(A\cap B)-P(A)$$

$$=0.6+0.1-0.5=0.2$$

The probability that one person, selected at random, reads magazine B is 0.2.

2.2

$$P(A)P(B)=0.5(0.2)=0.1=P(A\cap B)$$

Then the events A and B are independent events.

2.3