Assume you are working with a standard deck of 52 cards. There are 13 cards [tex]$(2,3,4,5,6,7,8,9,10$[/tex], jack, queen, king, and ace) in each of four suits (clubs, diamonds, hearts, and spades).
What is [tex]$P$[/tex](Jack [tex]$\cap$[/tex] Heart) if you draw one card?
A. 0
B. [tex]$\frac{17}{52}$[/tex]
C. [tex]$\frac{4}{13}$[/tex]
D. [tex]$\frac{1}{52}$[/tex]
Answer (2)
Determine the number of cards that are both a Jack and a Heart: 1.
Divide this number by the total number of cards in the deck: 52 1 .
Express the probability as a fraction: 52 1 .
Explanation
Understand the problem We are asked to find the probability of drawing a card that is both a Jack and a Heart from a standard 52-card deck. Let's break down the problem to understand it better.
Identify the favorable outcome In a standard deck of 52 cards, there are four suits: clubs, diamonds, hearts, and spades. Each suit has 13 cards, including one Jack. Therefore, there is only one card that is both a Jack and a Heart.
Calculate the 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, there is 1 favorable outcome (the Jack of Hearts) and 52 total possible outcomes (all the cards in the deck).
State the final answer Therefore, the probability of drawing the Jack of Hearts is: P ( J a c k ∩ He a r t ) = 52 1 So, the probability of drawing a card that is both a Jack and a Heart is 52 1 .
Examples
This type of probability calculation is fundamental in games involving cards, such as poker or blackjack. For instance, understanding the probability of drawing specific cards helps players make informed decisions about betting and strategy. Knowing the likelihood of drawing a particular card can also be applied in scenarios like quality control in manufacturing, where you might want to determine the probability of selecting a defective item from a batch.
The probability of drawing a Jack that is also a Heart from a standard deck of 52 cards is 52 1 . I chose option D. This outcome reflects the presence of only one Jack of Hearts among the 52 cards.
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