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.
The probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{{10}},\,\frac{3}{5}$ and $\frac{1}{4}.$ The probability that the student fails in the examination is
Three coins are tossed once. Find the probability of getting at most $2$ heads.
Two dice are thrown. The events $A,\, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$
State true or false $:$ (give reason for your answer)
Statement : $A$ and $C$ are mutually exclusive
If two dice are thrown simultaneously then probability that $1$ comes on first dice is
From a book containing $100$ pages, one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is $11$, is