Embibe Experts Solutions for Exercise 2: EXERCISE 14.2

$A$ draws two cards with replacement from a deck of $52$ cards and $B$ throws a pair of dice. The chance that $A$ gets both cards of same suit and $B$ gets total of $6$ is

Two dice are thrown together. The probability that at least one will show its digit $6$ is

The probability that $A$ speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact, is

If $P\left(B\right)=\frac{3}{4},P\left(A\cap B\cap \overline{C}\right)=\frac{1}{3}$ and $P\left(\overline{A}\cap B\cap \overline{C}\right)=\frac{1}{3}$. Find $P\left(B\cap C\right)$.

Five horses are in race. Mr. $A$ selects two of the horses at random and bets on them. Find the probability that Mr. $A$ selected the winning horse.

If $A$ and $B$ are two independent events, then $A$ and $\overline{B}$  are

The odds against a certain event is $5:2$ and the odds in favour of another event is $6:5$. If both the events are independent, then the probability that at least one of the events will happen is

If $A$ and $B$ are two independent events such that $P\left(\overline{A}\cap B\right)=\frac{2}{15}$ and $P\left(A\cap \overline{B}\right)=\frac{1}{6}$, then find $P\left(B\right)$.