Question

If a card is drawn from a pack of $52$ cards. Find the probability of getting a card bearing the number between $2$ and $5$ including $2$ and $5$:

• A. $\frac{3}{13}$
• B. $\frac{4}{13}$
• C. $\frac{5}{13}$
• D. $\frac{6}{13}$

Answer 1

The correct option is B $\frac{4}{13}$

$\Rightarrow$ Let C be the event that card drawn bears number between $2$ and $5$ including $2$ and $5$

∴ Number of cards between $2$ and $5$ including $2$ and $5$ is $4$ cards.

∴ There are $4$ types of cards i.e. Spades, Diamonds, Clubs and Hearts.

∴ The total no. of cards between $2$ and $5$ including $2$ and $5$ is $4\times$ $4$ = $16$

∴ n (C) $=$ $16$

$\Rightarrow$ P (C) = $\frac{n\left(C\right)}{n\left(S\right)}$

∴ P (C) $=$ $\frac{16}{52}$

∴ P (C) $=$ $\frac{4}{13}$