If Julie draws a card from a standard deck of well-shuffled playing cards, what is the probability that he draws either an ace or a heart?
In a standard deck there are 13 hearts and 4 aces. However one the hearts is an ace. So we're talking 13+4=17 cards, but then subtract one (16) for the ace of hearts that would be repeated if counting the hearts and aces separately.
So 16/52 is the probability. This can be reduced to 4/13.
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To find the probability that Julie draws either an ace or a heart, we need to determine how many favorable outcomes there are and divide it by the total number of possible outcomes.
Let's break it down step by step:
Step 1: Determine the number of favorable outcomes.
- Number of aces in a standard deck: There are four aces in a deck (one ace for each suit: hearts, clubs, diamonds, and spades).
- Number of hearts in a standard deck: There are 13 hearts in a deck (one heart for each value: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king).
- However, we need to subtract the ace of hearts since it has already been counted as an ace.
- So, the total number of favorable outcomes (either an ace or a heart) is 4 (number of aces) + 13 (number of hearts) - 1 (ace of hearts) = 16.
Step 2: Determine the total number of possible outcomes.
- In a standard deck of playing cards, there are 52 cards.
Step 3: Calculate the probability.
- Probability = Number of favorable outcomes / Total number of possible outcomes.
- Probability = 16 / 52.
- Simplifying, we get: Probability = 4 / 13.
Therefore, the probability that Julie draws either an ace or a heart is 4/13 or approximately 0.308