A card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace
Let $E$ be the event in which the card drawn is an ace.
since there are $4$ ace in a pack of $52$ cards, $n(E)=4$
$\therefore P(E)=\frac{\text { Number of outcomes favourable to } E}{\text { Total mumber of possible outcomes }}=\frac{n(E)}{n(S)}=\frac{4}{52}=\frac{1}{13}$
In a game, a man wins $Rs.\,100$ if he gets $5$ or $6$ on a throw of a fair die and loses $Rs.\,50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is
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 box contains $6$ nails and $10$ nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a nail
The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins), is
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 $\leq 5$
Describe the events $B$ or $C$