The chances of three independent events X Y Z o... - JAMB Mathematics 1993 Question
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?
A
\(\frac{1}{8}\)
B
\(\frac{1}{24}\)
C
\(\frac{1}{12}\)
D
\(\frac{1}{4}\)
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Correct Option: 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}) = 1(\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})
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