A deck of cards contains 52 cards. These cards consist of four suits - hearts, spades, clubs, and diamonds. Each suit contains one of each of the following: $2,3,4,5,6,7,8,9,10$, jack, queen, king, and ace. Assume that one card is selected at random from a well-shuffled deck of cards.
-Find the probability that the card is not a picture card (i.e. not a jack, queen, or king).
A) $\frac{10}{13}$
B) $\frac{1}{4}$
C) $\frac{3}{13}$
D) $\frac{49}{52}$

Question

Quizplus · Accepted Answer

In each suit, there are 3 picture cards (jack, queen, king) and 9 other cards (2 through 10, and ace). Therefore, the probability of not drawing a picture card is the number of non-picture cards (9 per suit) divided by the total number of cards in one suit (13), which simplifies to $\frac{9}{13}$. However, since the question involves all four suits, the correct calculation should consider the total number of cards. There are 12 picture cards in total (3 picture cards per suit times 4 suits) and 40 non-picture cards (10 non-picture cards per suit times 4 suits). Thus, the probability of not drawing a picture card is $\frac{40}{52}$, which simplifies to $\frac{10}{13}$.

A Deck of Cards Contains 52 Cards 2,3,4,5,6,7,8,9,102,3,4,5,6,7,8,9,102,3,4,5,6,7,8,9,10 , Jack, Queen, King, and Ace

A Deck of Cards Contains 52 Cards $2,3,4,5,6,7,8,9,10$ , Jack, Queen, King, and Ace