If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a spade or 6?
I'll be glad to check your answer.
To determine the probability of selecting a spade or 6 from a standard deck of 52 cards, we need to first find the total number of favorable outcomes and then divide it by the total number of possible outcomes.
1. Total Number of Favorable Outcomes:
- Spades: There are a total of 13 spades in a deck.
- 6 of any suit: There are 4 suits, and each has one 6. So, there are 4 sixes in total.
To avoid double-counting, we need to subtract the intersection of the two occurrences (the 6 of spades):
- Intersection: There is one 6 of spades.
Therefore, the total number of favorable outcomes is 13 (spades) + 4 (sixes) - 1 (intersection) = 16.
2. Total Number of Possible Outcomes:
- Since there are 52 cards in a standard deck, the total number of possible outcomes is 52.
Now, we can calculate the probability of selecting a spade or 6 by dividing the total number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable Outcomes / Possible Outcomes
= 16 / 52
= 4 / 13
So, the probability of randomly selecting a card that is a spade or 6 from a well-shuffled standard deck of 52 cards is 4/13.