from an ordinary deck of 52 cards, a single card is selected random. what is the probability that it is a 10 or red card?
prob(10 or red)
= prob(10) + prob(red) - prob(10 AND red)
= 4/52 + 26/52 - 2/52
= 28/52
= 7/13
From an ordinary deck of 52 cards, a single card is selected random. What is the probability that it is a 10 or red card?
= prob(10) + prob(red) - prob(10 AND red)
= 4/52 + 26/52 - 2/52
= 28/52
= 7/13
So, the answer is 7/13.
Credits go to Reiny for helping.
To find the probability of selecting a 10 or red card from an ordinary deck of 52 cards, we need to determine the number of favorable outcomes (cards that meet the criteria) and the total number of possible outcomes (all the cards in the deck).
1. Determine the number of favorable outcomes:
- There are a total of four 10 cards in a deck (10 of hearts, 10 of diamonds, 10 of clubs, 10 of spades).
- There are a total of 26 red cards in a deck (13 hearts and 13 diamonds).
Since we are interested in cards that are either a 10 or red, we should count only unique cards. Therefore, we will not include the 10 of hearts and 10 of diamonds in our count for red cards (to avoid duplication).
So, the number of favorable outcomes (10 or red cards) = 4 (10 cards) + 26 (red cards) - 2 (common cards) = 28.
2. Determine the total number of possible outcomes:
- A standard deck contains 52 cards.
3. Calculate the probability:
- Probability = Number of favorable outcomes / Total number of possible outcomes.
- Probability = 28 / 52 = 7/13.
Therefore, the probability of randomly selecting a 10 or red card from a standard deck of 52 cards is 7/13, or approximately 0.538 (rounded to three decimal places).