Question

An ordinary deck of cards contains 52 cards divided into four suits. Imagine choosing a card at random from a thoroughly mixed deck. Consider the event that the denomination of the chosen card is at most 4 (counting aces as 14). What is the probability of this event?

a) 1/2
b) 2/3
c) 1/3
d) 1/4

Answer 1

The probability of selecting a card with a denomination of at most 4 from a well-shuffled deck of 52 cards, counting aces as 14, is 1/4 (option d), as there are 12 such cards out of 52 total cards.

Step-by-step explanation:

The question asks for the probability of selecting a card with a denomination of at most 4 from a standard deck, counting aces as 14. In a well-shuffled deck of 52 cards with four suits (clubs, diamonds, hearts, spades), there are 3 denominations below 4 (2, 3, 4) for each suit.

Therefore, there are 3 cards per suit × 4 suits = 12 desirable cards. To get the probability, we divide the number of desirable outcomes by the total number of possible outcomes:

Probability = Number of desirable cards / Total number of cards

Probability = 12 / 52

When simplified, Probability = 3 / 13, which is approximately 1/4 (option d).