To find the probability that all 5 cards dealt from a standard deck of 52 cards are hearts, we can break it down step-by-step.
Firstly, there are 13 hearts in a deck of 52 cards. The probability of the first card being a heart is:
- Probability of 1st card: 13/52
Once the first card is drawn, there are now 12 hearts left and only 51 cards remaining in the deck. Thus, the probability of the second card being a heart is:
- Probability of 2nd card: 12/51
Continuing this process, the probabilities for the subsequent cards are:
- Probability of 3rd card: 11/50
- Probability of 4th card: 10/49
- Probability of 5th card: 9/48
Now, to find the total probability that all 5 cards are hearts, we multiply these probabilities together:
Overall Probability = (13/52) * (12/51) * (11/50) * (10/49) * (9/48)
Calculating this gives us:
- Overall Probability ≈ 0.000495
So, the probability that all 5 cards drawn from a standard deck of 52 cards are hearts is approximately 0.0495% or about 1 in 2023.