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Question

Mathematics Question on Probability

If A and B are two events of a sample space S such that P(A) = 0.2, P(B) = 0.6 and P(A | B) = 0.5 then P(A?| B)=

A

12\frac{1}{2}

B

512\frac{5}{12}

C

516\frac{5}{16}

D

1621\frac{16}{21}

Answer

12\frac{1}{2}

Explanation

Solution

P(A)=0.2,P(B)=0.6P\left(A\right)=0.2, P\left(B\right)=0.6
⇒ P(A∣B)=0.5\Rightarrow\, P\left(A |B\right)=0.5
P(A∩B)P(B)=0.5\frac{P\left(A\cap B\right)}{P\left(B\right)}=0.5
⇒ P(A∩B)=0.5(P(B))=(0.5)(0.6)=0.3\Rightarrow\, P\left(A\cap B\right)=0.5\left(P\left(B\right)\right)=\left(0.5\right)\left(0.6\right)=0.3
P(A′∣B)=P(A′∩B)P(B)=P(B)−P(A∩B)P(B)P\left(A ' | B\right)=\frac{P\left(A'\cap B\right)}{P\left(B\right)}=\frac{P\left(B\right)-P\left(A\cap B\right)}{P\left(B\right)}
=0.6−0.30.6=0.30.6=36=12=\frac{0.6-0.3}{0.6}=\frac{0.3}{0.6}=\frac{3}{6}=\frac{1}{2}