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The chances of three independent events X, Y, Z occurring ar...

The chances of three independent events X, Y, Z occurring are 12, 23, 14 respectively. What are the chances of Y and Z only occurring?

A.

18

B.

124

C.

112

D.

14

Correct answer is C

Chance of x = 12

Change of Y = 23

Chance of Z = 14

Chance of Y and Z only occurring

= Pr (Y ∩ Z ∩ Xc)

where Xc = 1 - Pr(X)

1 - 12 = 12

= Pr(Y) x Pr(Z) x Pr(Xc)

= 23 x 14 x 12

= 112