Question

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

• A. $\frac{1}{52}$
• B. $\frac{9}{13}$
• C. $\frac{6}{13}$
• D. $\frac{1}{13}$

Answer 1

Answer: (B)

$\frac{9}{13}$

Total number of cards in a deck $=52$

Number of diamond cards $=13$

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

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

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

[Since, $1$ king is already included in the $13$ diamonds so, here we will take number of kings is $3$.]

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

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

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