When drawing four cards, where you do NOT replace a card before drawing another card, what is the probability of drawing "four of a kind"?
Can you show me the steps.
well, there are 52 cards in the deck, 13 of each suit
4 of each kind, like four kings
so what is the probability of drawing four kings?
4/52 *3/51*2/50 *1/49
multiply that by 13 because it could have been four threes or four sevens or whatever
To find the probability of drawing "four of a kind" when drawing four cards without replacing any card, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the total number of possible outcomes
When drawing the first card, there are 52 options. For the second card, there are 51 options remaining, and for the third card, 50 options remain. Finally, for the fourth card, there are 49 options remaining.
Therefore, the total number of possible outcomes is calculated as:
52 * 51 * 50 * 49 = 649,7400
Step 2: Determine the number of favorable outcomes
For a "four of a kind," we need to choose one specific rank out of the four available (one for each suit). There are 13 different ranks to choose from.
Additionally, for the fifth card, we have to choose any one of the remaining 48 cards.
The number of favorable outcomes is calculated as:
13 * 48 = 624
Step 3: Calculate the probability
The probability of drawing "four of a kind" is given by:
Number of favorable outcomes / Total number of possible outcomes
Therefore, the probability is:
624 / 649,7400 = 0.0009604 or approximately 0.096%
So, the probability of drawing "four of a kind" is approximately 0.096%.
Please note that these calculations assume that the deck of cards is well-shuffled and has not been tampered with.