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.
A bag contains $9$ discs of which $4$ are red, $3$ are blue and $2$ are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be yellow.
The probabilities of a problem being solved by two students are $\frac{1}{2},\frac{1}{3}$. Then the probability of the problem being solved is
Two fair dice are tossed. Let $A$ be the event that the first die shows an even number and $B$ be the event that the second die shows an odd number. The two event $A$ and $B$ are
The number $1,\,2,\,3$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly, A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.
Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number ', $B$ be the event 'getting an odd number '. Write the sets representing the events $^{\prime}$ not $A\,^{\prime}$.