Question

a) Among University students it is known that 24% of students have a

Visa card, 32% have a Master card and 12% of student have both cards.

(1) What proportion of students has a Visa or a Master card?

(2) What proportion of students have only Visa or only Master card?

b)

Suppose that A and B are two events with P(A) =.4 and P(A∪B) = .7.

(3) For what values of P(B) would A and B be mutually exclusive?

(4) For what values of P(B) would A and B be independent?

Answer 1

a)

Here we have

P(visa) = 0.24, P(master) = 0.32, P(visa and master) = 0.12

(1)

The proportion of students has a Visa or a Master card is

P(visa or master) = P(visa) + P(master) - P(visa and master) = 0.24 + 0.32 - 0.12 = 0.44

Answer: 0.44

(2)

P(only Visa) = P(visa) - P(visa and master) = 0.24 - 0.12 = 0.12

P(only master) = P(master) - P(visa and master) = 0.32 - 0.12 = 0.20

The proportion of students have only Visa or only Master card is

P(only Visa or only Master) = P(only Visa) + P(only master) = 0.12 + 0.20 = 0.32

Answer: 0.32

(b)

If A and B are mutually exclusive then

P(A n B) = 0

Now,

P(A U B) = P(A) + P(B)

0.7 = 0.4 + P(B)

P(B) = 0.3

Answer: P(B) = 0.3

(4)

If A and B are independent then

Now,

Answer: P(B) = 0.5