Question

One card is drawn from a well-shuffled deck of $52$ cards. Find the probability of getting neither a diamond nor a jack.

• A. $\frac{8}{13}$
• B. $\frac{9}{13}$
• C. $\frac{6}{13}$
• D. $\frac{7}{26}$

Answer 1

The correct option is B $\frac{9}{13}$

Number of diamond cards $=13$

Total number of non-diamond cards out of $52$ cards $=52-13=39$

Number of jack cards out of $52$ cards $=4$

Number of jack cards in each of three suits namely hearts, spades, and clubs $=3$

Since, $1$ jack is already included in the $13$ diamonds so, here we will take number of jacks is $3$.

Neither a diamond nor a jack $=39-3=36$

$P$ (getting a neither a diamond nor a jack) $=$ $\frac{\text{Number of favourable outcomes}}{\text{Number of total possible outcomes}}$

$=\frac{36}{52}=\frac{9}{13}$