If A and B are two events such that P(not A)=(7)/(10), P( not B)=(3)/(10) and P(A B)=(3)/(14) , then what is P(B A) equal to?

Correct answer: D. (1)/(2) aligned & P(not A)=(7)/(10), P(not B)=(3)/(10), P(A / B)=(3)/(14) & arrow Now, P(A / B)=(P(A B))/(P(B)) P(A B)=P(B) P(A / B) & P(A B)=[1-P(not B)] P(A / B)=(1-(3)/(10))((3)/(14)) & =(7)/(10) × (3)/(14)=(3)/(20) & arrow P(B / A)=(P(A B))/(P(A))= P(A B) 1-P(not A) =((3)/(20))/(1-(7)/(10)) & =(3)/(20) × (10)/(3) & P(B / A)=1 / 2 aligned

NDA 2021

Exam: NDA
Year: 2021
Subject: Mathematics
Chapter: Probability

NDA 2021 · Mathematics · Probability

If A and B are two events such that P(not A)=(7)/(10), P( not...

A

and

B

are two events such that

P(\operatorname{not} A)=\frac{7}{10}, P(

not

B)=\frac{3}{10}

and

P(A \mid B)=\frac{3}{14}

, then what is

P(B \mid A)

equal to?

Options

A $\frac{11}{14}$
B $\frac{9}{14}$
C $\frac{1}{4}$
D $\frac{1}{2}$

Correct answer

D. $\frac{1}{2}$

Step-by-step solution

\begin{aligned} & P(\operatorname{not} A)=\frac{7}{10}, P(\operatorname{not} B)=\frac{3}{10}, P(A / B)=\frac{3}{14} \\ & \rightarrow \operatorname{Now}, P(A / B)=\frac{P(A \cap B)}{P(B)} \Rightarrow P(A \cap B)=P(B) P(A / B) \\ & \therefore P(A \cap B)=[1-P(\operatorname{not} B)] P(A / B)=\left(1-\frac{3}{10}\right)\left(\frac{3}{14}\right) \\ & =\frac{7}{10} \times \frac{3}{14}=\frac{3}{20} \\ & \rightarrow P(B / A)=\frac{P(A \cap B)}{P(A)}=\frac{P(A \cap B)}{1-P(\operatorname{not} A)}=\frac{\frac{3}{20}}{1-\frac{7}{10}} \\ & =\frac{3}{20} \times \frac{10}{3} \\ & \therefore P(B / A)=1 / 2\end{aligned}

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