Amit M Agarwal Solutions for Chapter: Fundamentals of Probability, Exercise 4: Target Exercises

$A$ and $B$ are two independent events. The probability that both $A$ and $B$ occur is $\frac{ 1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$. Then, the probability of the two events are respectively

Let $A$ and $B$ be two events such that $P\left(A\right)=0·3$ and $P\left(A\cup B\right)=0·8$. If $A$ and $B$ are independent events, then $P\left(B\right)$ is equal to

Two dice are thrown together first and secondly three dice are thrown together. Then, the probability that the total in the first throw is $4$ or more and at the same time the total in the second thrown is $6$ or more, is

The probability that a man will live $10$ more years is $\frac{1}{4}$ and the probability that his wife will live $10$ more years is $\frac{1}{3}$. Then, the probability that none of them will be alive after $10$ years

A fair coin is tossed. If the result is a head, a pair of fair dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well-shuffled pack of 11 cards numbered $2,3,4,\dots ,12$ is picked up and the number on the card is noted. The probability that the noted number is $7$ or $8,$ is

A pair of dice is rolled together till a sum of either $5$ or $7$ is obtained. The probability that $5$ comes before $7$, is

A sample space consists of three mutually independent and equally likely events. The probability of happening of each one of them is equal to

Let, $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happens is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2}$.Then