One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.
A die has six faces that are numbered from $1$ to $6,$ with one number on each face. Let us denote the red, white, and blue dices as $R$, $W$, and $B$ respectively.
According, when a die is selected and then rolled, the sample is given by
$S =\{ R1,\, R 2$, $R3, R 4$, $R 5,\, R6$, $W 1,\, W2$, $W 3,\, W 4$, $W 5,\, W 6$, $B1,\, B 2$, $B 3,\, B4$, $B5,\, B6\}$
Three coins are tossed once. Let $A$ denote the event ' three heads show ', $B$ denote the event ' two heads and one tail show ' , $C$ denote the event ' three tails show and $D$ denote the event 'a head shows on the first coin '. Which events are Compound ?
Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment
$A:$ $^{\prime}$ the sum is even $^{\prime}$.
$B:$ $^{\prime}$the sum is a multiple of $3$$^{\prime}$
$C:$ $^{\prime}$the sum is less than $4 $$^{\prime}$
$D:$ $^{\prime}$the sum is greater than $11$$^{\prime}$.
Which pairs of these events are mutually exclusive ?
Two coins are tossed. Let $A$ be the event that the first coin shows head and $B$ be the event that the second coin shows a tail. Two events $A$ and $B$ are
The probability of hitting a target by three marksmen are $\frac{1}{2},\,\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that one and only one of them will hit the target when they fire simultaneously, is
A die is thrown. Describe the following events : $A$ : a number less than $7.$ Find the $A \cup B$.