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 heart or 10?

http://www.jiskha.com/display.cgi?id=1459447095

hearts OR ten

= 13 + 4 - 1 = 16
(can't count the 10 of hearts twice)

continue

To determine the probability of randomly selecting a card that is either a heart or a 10 from a standard deck of 52 cards, we need to find the number of favorable outcomes and divide it by the total number of possible outcomes.

Number of favorable outcomes:
- There are 13 hearts in a deck (ace of hearts, 2 of hearts, etc. up to king of hearts).
- There are 4 tens in a deck (10 of hearts, 10 of diamonds, 10 of clubs, and 10 of spades).
- However, we need to account for the fact that one card, the 10 of hearts, is included in both counts. Therefore, we subtract 1 from the total.

Favorable outcomes = 13 + 4 - 1 = 16

Total number of possible outcomes:
A standard deck contains 52 cards.

Total possible outcomes = 52

Now, we can calculate the probability:

Probability = Favorable outcomes / Total possible outcomes
Probability = 16 / 52
Probability ≈ 0.3077

Therefore, the probability of randomly selecting a card that is a heart or a 10 from a standard deck is approximately 0.3077, or about 30.77%.

To find the probability of randomly selecting a card that is a heart or a 10, we need to determine the number of favorable outcomes and the total number of possible outcomes.

1. Number of favorable outcomes:
- Hearts: There are 13 hearts in a standard deck of 52 cards, so there are 13 favorable outcomes.
- Tens: There are four tens (10 of hearts, 10 of diamonds, 10 of clubs, and 10 of spades), so there are four favorable outcomes.
- There is one card, the 10 of hearts, that falls into both categories. Since we don't want to count it twice, we subtract one from the total favorable outcomes.
- Therefore, there are 13 + 4 - 1 = 16 favorable outcomes.

2. Total number of possible outcomes:
- A standard deck of 52 cards contains 52 total cards.

3. Now we can calculate the probability:
- Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
- Probability = 16 / 52
- Simplifying the fraction gives us the answer.

By dividing 16 by 52, we find that the probability of selecting a card that is either a heart or a 10 is approximately 0.3077, or 30.77%.