Question

The probability that Krishna will be alive $10$ years hence, is 7/15 and that Hari will be alive is 7/10. The probability both Krishna and Hari will be dead $10$ years hence, is:

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

Answer 1

The correct option is B $\frac{24}{150}$

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, $P\left(A^c\right)=\frac{8}{15}$ & $P\left(B^c\right)=\frac{3}{10}$

$\because P\left(A^c\right)=1-P\left(A\right)$

Both events are independent of each other

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

so, we want

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

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