If a two-card hand is dealt from a well-shuffled deck of 52 cards, what is the probability that the hand contains two kings?
That would simply be
(4/52)(3/51) = 1/221
or
C(4,2)/C(52,2) = 6/1326 = 1/221
You say simply! :) j/k...it makes sense now, thank you.
To find the probability of getting two kings in a two-card hand from a well-shuffled deck of 52 cards, we need to determine the number of favorable outcomes (two kings) and the total number of possible outcomes.
Let's break it down step by step:
Step 1: Determine the number of favorable outcomes.
There are a total of 4 kings in a deck of 52 cards. To get two kings, we need to choose 2 out of the 4 kings. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n - r)!)
where n is the total number of items, and r is the number of items to be chosen.
In this case, we have 4 kings (n=4) and we want to choose 2 kings (r=2).
C(4, 2) = 4! / (2!(4 - 2)!) = 6
So, there are a total of 6 combinations of two kings in a deck of 52 cards.
Step 2: Determine the total number of possible outcomes.
To find the total number of possible outcomes, we need to calculate the number of ways to choose any two cards from the 52-card deck.
This can be calculated using the combination formula:
C(n, r) = n! / (r!(n - r)!)
where n is the total number of items (52 in this case), and r is the number of items to be chosen (2 in this case).
C(52, 2) = 52! / (2!(52 - 2)!) = 1326
So, there are a total of 1326 combinations of choosing any two cards from a deck of 52 cards.
Step 3: Calculate the probability.
The probability of an event occurring is given by the formula:
Probability = Number of favorable outcomes / Total number of possible outcomes
In this case, the number of favorable outcomes is 6 and the total number of possible outcomes is 1326.
Probability = 6 / 1326 = 1 / 221
Therefore, the probability of getting two kings in a two-card hand from a well-shuffled deck of 52 cards is 1/221.