Question

A card is drawn from a well-shuffled deck of $52$ cards. Find the odds in favour of getting a face card.

• A. $\frac{7}{10}$
• B. $\frac{3}{10}$
• C. $\frac{1}{10}$
• D. $\frac{5}{10}$

Answer 1

Answer: (B)

$\frac{3}{10}$

Answer 2

When a card is drawn from a well-shuffled deck of $52$ cards, the number of possible outcomes is $52$. Now, let $S$ be the sample space. Then, $n(S) = 52$ Let $E$ be the event of getting a face card. Since there are $12$ face cards, we have $n(E) = 12$. $\therefore P\left(E\right) = \frac{n\left(E\right)}{n\left(S\right)}$ $= \frac{12}{52}$ $= \frac{3}{13}$ $\Rightarrow$ Odds in favour of getting a face card = \frac{P\left(E\right)}{\left\\{1-P\left(E\right)\right\\}} = \frac {3/13}{(1-\frac{3}{13})} $=\frac{3}{10}$.