Three coins are tossed. Describe Two events which are mutually exclusive.
When three coins are tossed, the sample space is given by
$S =\{ HHH , \,HHT , \,HTH ,\, HTT , \,THH , \,THT , \,TTH , \,TTT \}$
Two events that are mutually exclusive can be
$A:$ getting no heads and $B:$ getting no tails
This is because sets $A=\{T T T\}$ and $B=\{H H H\}$ are disjoint.
Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happen is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2}$ , then a value of $\frac{{P(E)}}{{P\left( F \right)}}$ is
The probability of a sure event is
A bag $x$ contains $3$ white balls and $2$ black balls and another bag $y$ contains $2$ white balls and $4$ black balls. A bag and a ball out of it are picked at random. The probability that the ball is white, is
The probability of getting a number greater than $2$ in throwing a die is
Let $A, B, C$ be three mutually independent events. Consider the two statements ${S_1}$ and ${S_2}$
${S_1}\,\,:\,\,A$ and $B \cup C$ are independent
${S_2}\,\,:\,\,A$ and $B \cap C$ are independent
Then