What is the probability that a card drawn randomly from a standard deck of 52 cards is a black five? Express your answer as a fraction in lowest terms or a decimal number rounded to three decimal places, if necessary.
Answer (2)
The probability of drawing a black five from a standard deck of 52 cards is 26 1 . This means that out of every 26 draws, on average, you would expect to draw a black five once. Therefore, the answer is 26 1 .
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Determine the number of black fives in a standard deck of 52 cards: 2.
Calculate the probability of drawing a black five: 52 2 .
Simplify the fraction to its lowest terms: 26 1 .
The probability of drawing a black five is 26 1 .
Explanation
Understand the problem and provided data We are asked to find the probability of drawing a black five from a standard deck of 52 cards. A standard deck has 52 cards, with 26 black cards (13 spades and 13 clubs) and 26 red cards (13 hearts and 13 diamonds). Each suit has one card of each rank, including a '5'. Therefore, there are two black fives: the 5 of spades and the 5 of clubs.
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 outcomes are drawing a black five, and the total possible outcomes are drawing any card from the deck.
Calculate the probability There are 2 black fives in the deck, and there are 52 total cards. Therefore, the probability of drawing a black five is: 52 2 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 52 ÷ 2 2 ÷ 2 = 26 1
State the final answer The probability of drawing a black five from a standard deck of 52 cards is 26 1 .
Examples
This type of probability problem is useful in understanding the likelihood of events in games of chance, such as card games. For example, if you're playing poker, knowing the probability of drawing specific cards can help you make informed decisions about betting and strategy. In this case, the probability of drawing a black five is 26 1 , which means that on average, you would expect to draw a black five once every 26 draws.
