A card is drawn from a shuffled deck of 52 cards. What's th probability that the card is a spade or a face card?
my interpretation of a face card is
either Jack, Queen, or King
number(spade or face)
= number(spade) + number(face) - number(spade AND face)
= 13 + 12 - 3 = 22
prob(spade or face) = 22/52 = 11/26
To find the probability that a card is a spade or a face card, we need to determine two things:
1. The number of favorable outcomes: The number of cards that are either spades or face cards (excluding the king of spades, since it is both).
2. The total number of possible outcomes: The total number of cards in the deck, which is 52.
Let's break it down step-by-step:
1. Calculate the number of spades:
- There are 13 spades in a deck.
2. Calculate the number of face cards:
- There are 4 face cards in each suit (jack, queen, and king).
- Since there are 4 suits, the total number of face cards is 4 x 3 = 12.
3. Calculate the number of cards that are both a spade and a face card:
- The king of spades is both a spade and a face card, so we subtract 1 from the total number of face cards: 12 - 1 = 11.
4. Determine the number of favorable outcomes (spades or face cards):
- Add the number of spades to the number of face cards: 13 + 11 = 24.
5. Determine the probability:
- Divide the number of favorable outcomes by the total number of possible outcomes: 24 / 52 = 6 / 13.
Therefore, the probability that the card drawn is a spade or a face card is 6/13.