The chances of three independent events X, Y, Z occurring are $\frac{1}{2}$ , $\frac{2}{3}$ , $\frac{1}{4}$ respectively. What are the chances of Y and Z only occurring?

$\frac{1}{8}$

$\frac{1}{24}$

$\frac{1}{12}$

$\frac{1}{4}$

Correct answer is C

Chance of x = $\frac{1}{2}$

Change of Y = $\frac{2}{3}$

Chance of Z = $\frac{1}{4}$

Chance of Y and Z only occurring

= Pr (Y ∩ Z ∩ Xc)

where Xc = 1 - Pr(X)

1 - $\frac{1}{2}$ = $\frac{1}{2}$

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

= $\frac{2}{3}$ x $\frac{1}{4}$ x $\frac{1}{2}$

= $\frac{1}{12}$

See all Mathematics questions & answers

See more JAMB questions & answers

The chances of three independent events X, Y, Z occurring are $\frac{1}{2}$ , $\frac{2}{3}$ , $\frac{1}{4}$ respectively. What are the chances of Y and Z only occurring?

Similar Questions

Aptitude Tests

The chances of three independent events X, Y, Z occurring are 12\frac{1}{2}, 23\frac{2}{3}, 14\frac{1}{4} respectively. What are the chances of Y and Z only occurring?

Similar Questions

Aptitude Tests

The chances of three independent events X, Y, Z occurring are $\frac{1}{2}$ , $\frac{2}{3}$ , $\frac{1}{4}$ respectively. What are the chances of Y and Z only occurring?