uestion: Five cards are dealt from standard deck of 52 cards, what is the probability of being dealt 3 kings?
Here is what I have
P(3 kings)=
C(4,3) = 3 out of 4 kings being dealt
C(48,2 = 2 out of remaning cards to complete 5 card deal
C(52,5) = 5 cards dealt out of 52 card deck.
C(4,3) = 4
C(48,2) = 48!
2!(48-2)!= 48X47/2 = 24X47=1128
C(52,5) = 2598960
P(3KINGS) = 47 / 108290
Correct?
Correct!
To calculate the probability of being dealt 3 kings from a standard deck of 52 cards, you need to use the concept of combinations.
First, we need to calculate the number of ways to choose 3 out of the 4 kings. This can be calculated using the combination formula: C(4,3) = 4. This means there are 4 ways to choose 3 kings from the 4 available.
Next, we need to calculate the number of ways to choose 2 more cards from the remaining 48 cards in the deck. We can use the combination formula again: C(48,2) = 48! / (2! * (48-2)!) = 1128. This means there are 1128 ways to choose 2 additional cards from the remaining 48 cards.
Now, we need to calculate the total number of ways to deal 5 cards from a deck of 52 cards. This can be calculated using the combination formula as well: C(52,5) = 52! / (5! * (52-5)!) = 2598960. This means there are 2598960 possible combinations of dealing 5 cards from the deck.
Finally, we can calculate the probability of being dealt 3 kings by dividing the number of favorable outcomes (3 kings and 2 more cards) by the total number of possible outcomes (5 cards from the deck).
P(3 kings) = (4 * 1128) / 2598960 ≈ 0.0017154
So, the probability of being dealt 3 kings is approximately 0.0017154.