The probabilities that A and B will die withi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $P(A)$ be the probability that $A$ dies $= p$,so $P(A') = 1 - p$ is the probability that $A$ is alive.Let $P(B)$ be the probability that $B$ d

Vedclass · Accepted Answer

$p + q - 2pq$

Vedclass · Answer

(B) Let $P(A)$ be the probability that $A$ dies $= p$,so $P(A') = 1 - p$ is the probability that $A$ is alive.Let $P(B)$ be the probability that $B$ dies $= q$,so $P(B') = 1 - q$ is the probability that $B$ is alive.We want the probability that only one of them is alive at the end of the year.This happens if ($A$ is alive and $B$ dies) or ($B$ is alive and $A$ dies).Required probability $= P(A' \cap B) + P(B' \cap A)$Since the events are independent,this is equal to $P(A')P(B) + P(B')P(A)$.$= (1 - p)q + (1 - q)p$$= q - pq + p - pq$$= p + q - 2pq$.

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively. Then,the probability that only one of them will be alive at the end of the year is

Similar Questions

Person $A$ can solve $90 \%$ of the problems given in the book and Person $B$ can solve $70 \%$. Then,the probability that at least one of them will solve the problem selected at random from the book is

$A$ bag contains $3$ red and $5$ black balls and a second bag contains $6$ red and $4$ black balls. $A$ ball is drawn from each bag. The probability that one is red and the other is black is:

If $A$ and $B$ are any two events,then $P(\bar{A} \cap B) = $

Two dice are thrown simultaneously. What is the probability of obtaining a sum of the numbers less than $11$?

$A$ fair coin and an unbiased die are tossed. Let $A$ be the event 'head appears on the coin' and $B$ be the event '$3$ on the die'. Check whether $A$ and $B$ are independent events or not.

Vedclass Test Series

Exam Paper Generator

Online Exam Module