Question

In a deck of playing cards, 2 new suits are introduced which are red and black in color respectively. If the number and types of cards in the new suits are same as the standard suits. Find the probability that I will get a face card on a random draw of 1 card. Also find the probability if the new suits were not introduced

• A. $\frac{4}{13},\frac{4}{13}$
• B. $\frac{3}{13},\frac{3}{13}$
• C. $\frac{6}{13},\frac{3}{13}$
• D. $\frac{8}{13},\frac{3}{13}$

Answer 1

The correct option is B

$\frac{3}{13},\frac{3}{13}$

If new suits were introduced total number of cards in a deck would become 52 + (2 $\times$13) = 78
Face cards are J, Q and K. There are 6 suits now (4 old +2 new) So total number of face cards would become 3$\times$6 = 18
Probability of getting a face card = $\frac{18}{78}$ = $\frac{3}{13}$
If new suits were not introduced, total number of cards = 52
Number of face cards = 3$\times$4 =12(since new suits are not introduced)
Probability of getting a face card = $\frac{12}{52}$ = $\frac{3}{13}$
It is interesting to note that probabilities are same.