If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability of getting three queens and one king.

Answer 1

To find the probability of getting three queens and one king, we need to calculate the number of favorable outcomes and the number of possible outcomes.

Number of favorable outcomes:
There are 4 queens and 4 kings in a deck of 52 cards. To get three queens and one king, we choose 3 queens out of 4 and 1 king out of 4. The number of favorable outcomes is given by:
Number of favorable outcomes = (Number of ways to choose 3 queens) * (Number of ways to choose 1 king)
Number of favorable outcomes = (4C3) * (4C1) = (4) * (4) = 16

Number of possible outcomes:
When we are dealing from a shuffled deck of 52 cards, the number of possible outcomes is given by the number of ways we can choose 3 cards out of the 52. Mathematically, this is expressed as:
Number of possible outcomes = 52C3 = (52 * 51 * 50) / (3 * 2 * 1) = 22,100

Therefore, the probability of getting three queens and one king is given by:
Probability = Number of favorable outcomes / Number of possible outcomes = 16 / 22,100 ≈ 0.000724

Thus, the probability of getting three queens and one king when dealt 3 cards from a shuffled deck of 52 cards is approximately 0.000724.