A card is drawn from a deck of cards. What is the probability that the card is a jack or ace?
Answer (2)
Calculate the probability of drawing a Jack: 52 4 .
Calculate the probability of drawing an Ace: 52 4 .
Add the probabilities since the events are mutually exclusive: 52 4 + 52 4 = 52 8 .
Simplify the fraction: 13 2 .
Explanation
Problem analysis We are asked to find the probability of drawing a jack or an ace from a standard deck of 52 cards. A standard deck has 4 jacks and 4 aces.
Probability definition The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Calculate probabilities of drawing Jack and Ace The probability of drawing a jack is the number of jacks divided by the total number of cards: P ( J a c k ) = 52 4 The probability of drawing an ace is the number of aces divided by the total number of cards: P ( A ce ) = 52 4
Calculate probability of drawing Jack or Ace Since drawing a jack and drawing an ace are mutually exclusive events (you cannot draw a card that is both a jack and an ace at the same time), the probability of drawing a jack or an ace is the sum of their individual probabilities: P ( J a c k or A ce ) = P ( J a c k ) + P ( A ce ) = 52 4 + 52 4 = 52 8
Simplify the fraction Simplify the fraction: 52 8 = 13 2
Final answer Therefore, the probability of drawing a jack or an ace from a standard deck of cards is 13 2 .
Examples
Imagine you're playing a card game where you need either a Jack or an Ace to win. Calculating this probability helps you understand your chances of getting a winning card on your next draw. This is useful in games like poker or blackjack, where knowing the odds can inform your strategy.
The probability of drawing a jack or an ace from a standard deck of cards is 13 2 . This is calculated by adding the probabilities of drawing each card separately since they are mutually exclusive events. Therefore, the final result is 13 2 .
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