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%).