Probability of randomly selecting a 3 or a face card?

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02-06-2024
Mathematics

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Probability of randomly selecting a 3 or a face card?

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djben1424 djben1424 · Answer 1 · 2024-06-02T17:48:04-04:00

To find the probability of randomly selecting a 3 or a face card from a standard deck of 52 playing cards, follow these steps:

Identify the number of 3s in the deck:

There are 4 cards that are 3s (one for each suit: hearts, diamonds, clubs, and spades).

Identify the number of face cards in the deck:

Face cards are Jacks, Queens, and Kings. There are 3 face cards per suit, and there are 4 suits.

Therefore, there are 3 * 4 = 12 face cards in total.

Calculate the total number of favorable outcomes:

Since there are no 3s that are also face cards, the number of favorable outcomes is the sum of the number of 3s and the number of face cards:

4 + 12 = 16

Calculate the probability:

The probability (P) of selecting a 3 or a face card is the number of favorable outcomes divided by the total number of cards in the deck:

P = Number of favorable outcomes / Total number of cards = 16 / 52

Simplify the fraction:

Simplify 16 / 52 by dividing the numerator and the denominator by their greatest common divisor, which is 4:

16 / 52 = (16 ÷ 4) / (52 ÷ 4) = 4 / 13

Therefore, the probability of randomly selecting a 3 or a face card from a standard deck of 52 playing cards is 4/13 or approximately 0.3077 (30.77%).