Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • A and B are two events such that P(A)=1/2 and . Find: (i) P(A|B) (ii) P(B|A) (iii) P(A’|B) (iv) P(A’|B’)

A and B are two events such that P(A)=\frac{1}{2},P(B)=\frac{1}{2}\: \: and P(A \cap B)= \frac{1}{4}  
Find:
(i) P(A|B) (ii) P(B|A) (iii) P(A’|B) (iv) P(A’|B’)

Answers (1)

Given-

P(A)=\frac{1}{2},P(B)=\frac{1}{2}\: \: $and $P(A \cap B)= \frac{1}{4}

\\(i) P(A \mid B)=\frac{P(A \cap B)}{P(B)} \\=\frac{\frac{\frac{1}{4}}{1}}{3} \\=\frac{3}{4} \\(ii) P(B \mid A)=\frac{P(A \cap B)}{P(A)} \\=\frac{\frac{1}{4}}{2} \\=\frac{1}{2}

\begin{aligned} &\text { (iii) }\\ &\mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}\right)=\mathrm{P}\left(\frac{\mathrm{A}^{\prime} \cap \mathrm{B}}{\mathrm{P}(\mathrm{A})}\right)\\ &=\frac{\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \mathrm{U} \mathrm{B})}{\mathrm{P}(\mathrm{B})}\\ &=\frac{\frac{1}{3}-\frac{1}{4}}{\frac{1}{3}}\\ &=\frac{\frac{1}{12}}{\frac{1}{3}}\\ &=\frac{1}{4} \end{aligned}

iv)

\\ P\left(A^{\prime} \mid B'\right)=P\left(\frac{A^{\prime} \cap B^{\prime}}{P\left(B^{\prime}\right)}\right)=\frac{1-P(A U B)}{1-P(B)} \\\\ =\frac{1-[P(A)+P(B)-P(A \cap B)]}{1-P(B)} \\\\ =\frac{1-\left[\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right]}{1-\frac{1}{3}} \\\\ =\frac{1-\left[\frac{5}{6}-\frac{1}{4}\right]}{\frac{2}{3}} \\\\ =\frac{1-\frac{14}{24}}{\frac{2}{3}} \\\\ =\frac{\frac{10}{24}}{\frac{2}{3}} \\\\ =\frac{30}{48} \\\\ =\frac{5}{8}

 

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question