Question

Of 12,000 students, 3,000 have a Mastercard (M), 4,000 have a VISA (V ) and 1,500 have both.

Find the probability that a randomly selected student:

(a) Has a Mastercard.

(b) Has a VISA.

(c) Has both Mastercard and VISA.

(d) Has either Mastercard or VISA.

(e) Has a Mastercard but not VISA.

(f) Has a VISA but not Mastercard.

(g) Has neither Mastercard nor VISA.

Answer 1

(a)

P(Has a Mastercard) = P(M) = n(M) / Total = 3000/12000 = 0.25

(b)

P(Has a VISA) = P(V) = n(V) / Total = 4000/12000 = 0.3333

(c)

P(Has both Mastercard and VISA) = P(M V) = n(M V) / Total = 1500 / 12000 = 0.125

(d)

P(Has either Mastercard or VISA) = P(M V) = P(M) + P(V) - P(M V)

= 0.25 + 0.3333 - 0.125

= 0.4583

(e)

P(Has a Mastercard but not VISA) = P(M) - P(M V) = 0.25 - 0.125 = 0.125

(f)

P(Has a VISA but not Mastercard) = P(V) - P(M V) = 0.3333 - 0.125 = 0.2083

(g)

P(Has neither Mastercard nor VISA) = 1 - P(Has either Mastercard or VISA)

= 1 - 0.4583

= 0.5417