If you pick one card at random from a standard deck of 52 cards, what is the probability it will be a King?
A. $1 / 12$
B. $4 / 13$
C. $1 / 13$
D. $1 / 4$
Answer (2)
The probability of an event is the number of favorable outcomes divided by the total number of outcomes.
There are 4 Kings in a standard deck of 52 cards.
Calculate the probability of picking a King: 52 4 .
Simplify the fraction: 52 4 = 13 1 .
Explanation
Understand the problem We are asked to find the probability of drawing a King from a standard deck of 52 cards. A standard deck contains 4 Kings.
Define probability The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is drawing a King, and the total number of possible outcomes is the total number of cards in the deck.
Calculate the probability The number of Kings in the deck is 4, and the total number of cards is 52. Therefore, the probability of drawing a King is: P ( King ) = Total number of cards Number of Kings = 52 4
Simplify the fraction We can simplify the fraction 52 4 by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 52 4 = 52 ÷ 4 4 ÷ 4 = 13 1
State the final answer Therefore, the probability of drawing a King from a standard deck of 52 cards is 13 1 .
Examples
Consider a game where you win if you draw a King from a deck of cards. Knowing the probability of drawing a King helps you understand your chances of winning. In a standard deck of 52 cards, there are 4 Kings, so the probability of drawing a King is 52 4 , which simplifies to 13 1 . This means that, on average, you would expect to draw a King once every 13 tries.
The probability of drawing a King from a standard deck of cards is 13 1 . This is calculated by dividing the number of Kings (4) by the total number of cards (52). Therefore, the correct answer is option C: 13 1 .
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