Three coins are tossed. Describe Two events, which are not 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 not mutually exclusive can be
$A:$ getting three heads
$B:$ getting at least $2$ heads
ie. $A=\{H H H\}$
$B =\{ HHH , \,HHT , \,HTH ,\, THH \}$
This is because $A \cap B=\{H H H\} \neq \phi$
Seven chits are numbered $1$ to $7$. Three are drawn one by one with replacement. The probability that the least number on any selected chit is $5$, is
If three students $A, B, C$ independently solve a problem with probabilitities $\frac{1}{3},\frac{1}{4}$ and $\frac{1}{5}$ respectively, then the probability that the problem will be solved is
A die is thrown. Describe the following events : $A$ : a number less than $7.$ Find the $A \cup B$.
Two dice are thrown together. The probability that at least one will show its digit $6$ is
If $\frac{2}{11}$ is the probability of an event, what is the probability of the event $'$ not $A ^{\prime}$.