The probabilities of A and B dying in a year | vedclass

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

Question

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

Vedclass · Accepted Answer

$p + q - 2pq$

Vedclass · Answer

(B) Let $P(A) = p$ be the probability that $A$ dies,so $P(A') = 1 - p$ is the probability that $A$ lives.Let $P(B) = q$ be the probability that $B$ dies,so $P(B') = 1 - q$ is the probability that $B$ lives.The event that only one of them is alive at the end of the year means either ($A$ dies and $B$ lives) or ($B$ dies and $A$ lives).Since the events are independent,the required probability is $P(A \cap B') + P(B \cap A') = P(A) \cdot P(B') + P(B) \cdot P(A')$.Substituting the values: $p(1 - q) + q(1 - p) = p - pq + q - pq = p + q - 2pq$.

The probabilities of $A$ and $B$ dying in a year are $p$ and $q$ respectively. What is the probability that only one of them will be alive at the end of the year?

Similar Questions

$A$ container holds two balls. Both balls are black. If one white ball is added to the container and then one ball is drawn at random from the container,what is the probability that it is white?

$A$ coin is tossed again and again. If tail appears on the first three tosses, then the chance that head appears on the fourth toss is

If two dice are thrown, then the probability of getting coprime numbers on the dice is

$A$ person can hit a bird once in three attempts. If the person makes three attempts, what is the probability that the bird is hit (in $/27$)?

$A$ coin is tossed $3$ times. The probability of getting exactly two heads is

Vedclass Test Series

Exam Paper Generator

Online Exam Module