Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If A and B are two independent events with P(A) = 3/5 and P(B) = 4/9, then P (A′ ∩ B′) equals A.4/15 B. 8/45 C. 1/3 D. 2/9

If A and B are two independent events with P(A) = 3/5 and P(B) = 4/9, then P (A′ ∩ B′) equals
A.4/15
B. 8/45
C. 1/3
D. 2/9

 

Answers (1)

\begin{aligned} &\text { As } A \text { and } B \text { are independent } A^{\prime} \text { and } B^{\prime} \text { are also independent. }\\ &P\left(A^{\prime} \cap B^{\prime}\right)=P\left(A^{\prime}\right) \cdot P\left(B^{\prime}\right)\\ &\text { As we know, } \mathrm{P}\left(\mathrm{A}^{\prime}\right)=(1-\mathrm{P}(\mathrm{A})) \text { and } \mathrm{P}\left(\mathrm{B}^{\prime}\right)=(1-\mathrm{P}(\mathrm{B})\\ &\Rightarrow(1-\mathrm{P}(\mathrm{A})) \cdot(1-\mathrm{P}(\mathrm{B}))=\left(1-\frac{3}{5}\right)\left(1-\frac{4}{9}\right)\\ &=\left(\frac{2}{5}\right)\left(\frac{5}{9}\right)\\ &\Rightarrow\left(P\left(A^{\prime} \cap B^{\prime}\right)=\frac{2}{9}\right. \end{aligned}

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question