If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability of getting one queen and two kings.
To find the probability of getting one queen and two kings when dealt three cards from a shuffled deck of 52 cards, we need to calculate the number of successful outcomes (getting one queen and two kings) and divide it by the total number of possible outcomes (all possible combinations of three cards).
First, let's determine the number of successful outcomes:
There are four queens in a deck (one queen for each suit: hearts, diamonds, clubs, and spades). We need to choose one queen out of the four available options.
There are four kings in a deck (one king for each suit: hearts, diamonds, clubs, and spades). We need to choose two kings out of the four available options.
To calculate the number of successful outcomes, we can use the concept of combinations:
Number of successful outcomes = Number of ways to choose 1 queen from 4 queens * Number of ways to choose 2 kings from 4 kings
Number of successful outcomes = (4 C 1) * (4 C 2)
Number of successful outcomes = 4 * 6
Number of successful outcomes = 24
Now, let's determine the total number of possible outcomes:
We need to choose 3 cards from a deck of 52 cards.
Total number of possible outcomes = Number of ways to choose 3 cards from 52 cards
Total number of possible outcomes = (52 C 3)
Total number of possible outcomes = 22,100
Finally, we can calculate the probability:
Probability = Number of successful outcomes / Total number of possible outcomes
Probability = 24 / 22,100
Probability ≈ 0.0011 or 0.11%