Haryana Police Constable Model Paper 4

Formula used:
${}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}=\frac{\mathrm{n}!}{\left(\left(\mathrm{n}-\mathrm{r}\right)!\times \mathrm{r}!\right)}$
Calculation:Let S be the sample space then,
n(S) = number of way of selecting 1 card out of 52 card
$\Rightarrow \mathrm{n}\left(\mathrm{S}\right)={}^{52}{\mathrm{C}}_1=52$
Let E be the event of getting a diamond card
Total number of diamond card = 13
n(E) = ${}_{}^{13}{\mathrm{C}}_1^{}$ = 13
$\mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}(\mathrm{S}}$
⇒ P(E) = $\frac{13}{52}$ ⇒ $\frac{1}{4}$
∴ The probability of a diamond card is 1/4