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?
first king 4/52
second king 3/51
so
12/2652 = 1/221
To find the probability of getting two kings in a two-card hand from a standard deck of 52 cards, we need to determine two things:
1. The total number of possible two-card hands that can be dealt from a deck of 52 cards.
2. The number of favorable outcomes, i.e., the number of two-card hands that contain two kings.
Let's calculate these two values:
1. Total number of possible two-card hands:
To choose the first card, there are 52 options. After taking one card, there are 51 remaining for the second card. So, the total number of possible two-card hands is given by 52 * 51 = 2,652.
2. Number of two-card hands containing two kings:
There are 4 kings in a deck of 52 cards. To choose two kings, we use the combination formula, which is denoted as C(n, r) and calculated as n! / (r!(n-r)!), where n is the total number of items and r is the number of items chosen.
In this case, we need to choose 2 kings from a group of 4 kings, so the number of two-card hands with two kings is C(4, 2) = 4! / (2!(4-2)!) = (4 * 3) / (2 * 1) = 6.
Now, we can calculate the probability:
Probability of getting two kings = Number of two-card hands with two kings / Total number of possible two-card hands
= 6 / 2,652
= 0.00225989
Therefore, the probability of getting two kings in a two-card hand from a well-shuffled deck of 52 cards is approximately 0.00225989, or about 0.22%.