Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If P(A) = 3|10, P(B) = 2|5 and P(A ∪ B) = 3|5, then P(B|A) + P(A|B) equals A. 1|4 B. 1|3 C. 5|12 C. 7|2

If \begin{aligned} &P(A)=\frac{3}{10}, P(B)=\frac{2}{5} \text { and } P(A \cup B)=\frac{3}{5}\\ \end{aligned}, then P(B|A) + P(A|B) equals
A. 1|4
B. 1|3
C. 5|12
C. 7|2

Answers (1)

Given-

\begin{aligned} &P(A)=\frac{3}{10}, P(B)=\frac{2}{5} \text { and } P(A \cup B)=\frac{3}{5}\\ &\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B}) \text { [Additive Law of Probability] }\\ &\therefore \frac{3}{5}=\frac{3}{10}+\frac{2}{5}-P(A \cap B)\\ &\Rightarrow P(A \cap B)=\frac{3}{10}-\frac{1}{5}\\ &\Rightarrow P(A \cap B)=\frac{3-2}{10}\\ &\Rightarrow P(A \cap B)=\frac{1}{10}\\ &\text { As we know the Property of Conditional Probability: }\\ &\mathrm{P}(\mathrm{A} \mid \mathrm{B}) \times \mathrm{P}(\mathrm{B})=\mathrm{P}(\mathrm{A} \cap \mathrm{B})\\ &\Rightarrow P(A \mid B)=\frac{P(A \cap B)}{P(B)} \end{aligned}

\begin{aligned} &\mathrm{P}(\mathrm{B} \mid \mathrm{A}) \times \mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B} \cap \mathrm{A})\\ &\Rightarrow P(B \mid A)=\frac{P(B \cap A)}{P(A)}\\ &\text { Multiplying eq. (i) and (ii), we get }\\ &\therefore P(B \mid A)+P(A \mid B)=\frac{P(B \cap A)}{P(A)}+\frac{P(A \cap B)}{P(B)}\\ &=\frac{\frac{1}{10}}{\frac{3}{10}}+\frac{\frac{1}{10}}{\frac{2}{5}}\\ &=\frac{1}{3}+\frac{1}{10} \times \frac{5}{2}\\ &=\frac{4+3}{12}\\ &=\frac{7}{12} \end{aligned}

Hence, the Correct option is D

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question