Math probability question! Quick Points!?
Hey guys i just did a question on an exam that i wasn't really sure how to do:
Here's the question.
Out of a standard deck of 52 cards, 5 cards are chosen. What is the probability of choosing exactly 1 king and up to 2 aces ? my final answer was around... 0.3.
Can someone confirm if my answer is correct or not? THANKS
Points go to first person that answers. Steps + explanation included please
- ♣ K-Dub ♣Lv 61 decade agoFavorite Answer
There are 52C5 possible 5-card hands.
We need exactly one king. There are 4 kings to choose from. Otherwise, we have a 4-card hand with at most two aces and no kings.
no aces → 44C4 possible hands
one ace → 4C1 * 44C3 possible hands
two aces → 4C2 * 44C2 possible hands.
P(one king & at most two aces)
= 4 * [44C4 + 4 * 44C3 + 6 * 44C2] / 52C5
To check, observe that
P(exactly one king) = 4*48C4 / 52C5 ≈ .2995.
Taking into account that getting at least 3 aces in a 4-card hand is unlikely, the indicated answer appears to be consistent with being correct.
Hope this helps.