When a card is selected from a deck, find the probability of getting a diamond, a face card or a diamond, or a club and a king?
Are these one problem or several problems? Are the cards being replaced back in the deck after they are being picked? It makes a difference.
Diamond = 13/52 = 1/4
With the other situations, replacement makes a difference.
To find the probability of getting a specific event, we need to know the total number of outcomes and the number of favorable outcomes. Let's break down each part of the question and find the probabilities step by step.
1. Probability of getting a diamond:
In a standard deck of 52 playing cards, there are 13 diamonds. So, the probability of getting a diamond is:
Number of favorable outcomes (13 diamonds) / Total number of outcomes (52 cards) = 13/52 = 1/4.
2. Probability of getting a face card or a diamond:
A face card refers to Jacks, Queens, and Kings. In a standard deck, there are 3 face cards per suit, totaling to 12 face cards. As we found earlier, there are 13 diamonds in total. However, we shouldn't count the diamond face cards twice, so we need to subtract the 3 diamond face cards from the total count of face cards. Therefore, the total number of favorable outcomes is 12 + 13 - 3 = 22. Thus, the probability is:
Number of favorable outcomes (22) / Total number of outcomes (52) = 22/52 = 11/26.
3. Probability of getting a club and a king:
There are 4 kings in a standard deck, and 4 suits. So, the number of favorable outcomes is 4 (one king per suit). Since we have counted each possibility of the king being a club, the total number of outcomes remains 52. Hence, the probability is:
Number of favorable outcomes (4) / Total number of outcomes (52) = 4/52 = 1/13.
So, to recap:
- The probability of getting a diamond is 1/4.
- The probability of getting a face card or a diamond is 11/26.
- The probability of getting a club and a king is 1/13.