Question

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

• A. $\frac{11}{26}$
• B. $\frac{19}{26}$
• C. $\frac{6}{26}$
• D. $\frac{1}{26}$

Answer 1

Answer: (B)

$\frac{19}{26}$

Total number of cards in a deck $=52$

Number of clubs $=13$

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

Therefore, spades, hearts, and diamonds are the $39$ cards.
Cards of spades and clubs are black cards.

Number of black queen in black cards $=2$

Therefore, neither a club nor a black queen $=39-1=38$

[Since, $1$ black queen is already included in the $13$ clubs so, here we will take number of black queen is $1$.]

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

$=\frac{38}{52}=\frac{19}{26}$