Question

On a sample of 1,500 people in Sydney, 89 have no credit cards (event A), 750 have one (event B), 450 have two (event C) and the rest have more than two (event D). On the basis of the data, calculate each of the following.

a. The probability of Event A

b. The probability of Event D

c.The complement of event B

d. The complement of event C

e. The probability of event A or D.

Answer 1

From the given data

n(A) = 89

n(B) = 750

n(C) = 450

n(D) = 1500 - 89 - 750 - 450 = 211

n(S) = 1,500

a.

The probability of event A = P(A) = n(A) / n(S) = 89 / 1500 = 0.059

b.

The probability of event D = P(D) = n(D) / n(S) = 211 / 1500 = 0.141

c.

The complement of event B

n(B')= n(S) - n(B) = 1500 - 750 = 750

P(B') = n(B') / n(S) = 750 / 1500 = 0.5

d.

The complement of event C

n(C')= n(S) - n(C) = 1500 - 450 = 1050

P(C') = n(C') / n(S) = 1050 / 1500 = 0.7

e.

The probability of event A or D.

P(A or D) = P(A) + P(D) = 0.059 + 0.141 = 0.200