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3. Suppose you draw one card from a deck of 52 cards. What is the probability of drawing a Jack or an 8 ? Use the probability formula for mutually exclusive events,

Ask by Warner Adkins. in the United States
Feb 26,2025

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Answer

The probability of drawing a Jack or an 8 is 2/13.

Solution

There are 4 Jacks and 4 8s in a 52-card deck. Since drawing a Jack and drawing an 8 are mutually exclusive events (a card cannot be both a Jack and an 8), you add their individual probabilities: • Probability of a Jack: 4/52 • Probability of an 8: 4/52 Total probability = 4/52 + 4/52 = 8/52 = 2/13. Thus, the probability of drawing a Jack or an 8 is 2/13.

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The Deep Dive

To calculate the probability of drawing a Jack or an 8 from a standard deck of 52 cards, you can use the formula for mutually exclusive events. There are 4 Jacks and 4 eights in a deck. Therefore, the total number of favorable outcomes is 4 (Jacks) + 4 (eights) = 8. The probability is then calculated as the number of favorable outcomes divided by the total number of outcomes: P(Jack or 8) = 8/52 = 2/13, or approximately 0.154, which means there's about a 15.4% chance of drawing a Jack or an 8. When you'd like to impress your friends at game night, remember that a deck of cards isn't just for Poker or Solitaire; it's a treasure trove of probability lessons! You can even challenge them to calculate other card combinations, exploring the odds of drawing pairs, flushes, or even full houses in different games. Next time you pick up a deck, think of all the mathematical fun waiting to be unleashed!

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