Question

From a deck of $52$ cards, Bairstow picks up one card at random. What is the probability that he draws a red non-face card?

• A. $\frac{1}{2}$
• B. $\frac{3}{26}$
• C. $\frac{10}{13}$
• D. $\frac{5}{13}$

Answer 1

The correct option is D $\frac{5}{13}$

Suppose, $\text{E}$ is an event of drawing a red non-face card from a pack of $52$ cards.

Total number of possible outcomes= Total number of cards= $52$

In a deck of $52$ cards, for each of the four suits, we have $10$ non-face cards as out of $13$ cards in each suits, we need to eliminate $3$ face cards (Jack, King, Queen). And, we have $2$ red suits (diamonds, hearts). Thefore, the number of red non-face cards is $10\times 2=20$.

$\therefore$ Number of favorable outcomes= Number of red non-face cards= $20$

Hence,

$\text{P (E)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P (E)}=\frac{\text{Number of red non-face cards}}{\text{Total number of cards}}$

$\Rightarrow \text{P (E)}=\frac{20}{52}=\frac{4\times 5}{4\times 13}=\frac{5}{13}$

$\therefore$ The probability of drawing a red non-face card from a pack of $52$ cards is $\frac{5}{13}$.