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