A card is drawn from a well shuffled deck of playing cards. Find the probability of getting a red or a face card. Give the answer accurate to two decimal places.
Question
A card is drawn from a well shuffled deck of playing cards. Find the probability of getting a red or a face card. Give the answer accurate to two decimal places.
Solution
To find the probability of getting a red or a face card, we need to determine the number of favorable outcomes and the total number of possible outcomes.
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Determine the number of favorable outcomes:
- There are 26 red cards in a deck (13 hearts and 13 diamonds).
- There are 12 face cards in a deck (3 face cards in each suit: Jack, Queen, and King).
- However, we need to subtract the 6 cards that are both red and face cards (2 red face cards in each suit: Jack, Queen, and King).
- So, the number of favorable outcomes is 26 + 12 - 6 = 32.
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Determine the total number of possible outcomes:
- A standard deck of playing cards contains 52 cards.
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Calculate the probability:
- Probability = Number of favorable outcomes / Total number of possible outcomes.
- Probability = 32 / 52 = 0.6154 (rounded to four decimal places).
Therefore, the probability of drawing a red or a face card from a well-shuffled deck of playing cards is approximately 0.62 (rounded to two decimal places).
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