Question

Tne probability that Krishna will be alive $10$ years is $\frac{7}{15}$ and that Hari will be alive is $\frac{7}{10}$. The probability that both Krishna and Hari will be dead is -

• A. $\frac{21}{150}$
• B. $\frac{24}{150}$
• C. $\frac{49}{150}$
• D. $\frac{56}{150}$

Answer 1

The correct option is A $\frac{21}{150}$

Let $A$ & $B$ are events

that $A=$ krishna alive

$B=$ Hari alive

So given that $P\left(A\right)=\frac{7}{15}$

& $P\left(B\right)=\frac{7}{10}$

So. $P\left(A^{\prime }\right)=\frac{8}{15}$ & $P\left(B^{\prime }\right)=\frac{3}{10}$

$\because P\left(A^{\prime }\right)=1-P\left(A\right)$

Both event are independent from each other

So. $P(A\cap B)=P\left(A\right).P\left(B\right)$

So we want.

$P(A^{\prime }\cap B^{\prime })=p\left(A^{\prime }\right).P\left(B^{\prime }\right)$

$=\frac{8}{15}\times \frac{3}{10}=\frac{24}{150}$