Four cards are drawn from a pack of 52 cards.What is the probability that no two cards are of equal value?Probability

3 Answers

joshmrusso's profile pic

joshmrusso | Student, Undergraduate | (Level 1) eNoter

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In this problem you are just asking what the probability is. It doesn't seem that this is a clear question in that in drawing four cards out of a fifty-two card deck you have 52 choose 4 outcomes possible (or 270,725). Now, if you are wanting to know what the probability of getting a specific hand of four cards is you would need to take your one hand and divide it by the total number of outcomes.

1/(52 choose 4) which is approximately 3.69378521 × 10^-6.

Or say you want to know your chances of drawing the King of Hearts, you would need to find out how many different hands have the King of Hearts and divide that by the total number of outcomes.

Number of hands with King of Hearts. The King of Hearts is given so you have three more cards to choose to have a hand of four, so

51 choose 3 = 20,825

then (51 choose 3)/(52 choose 4) which is apporximately 0.0769230769
or 7.69% chance of drawing the King of Hearts.

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eventulay | (Level 1) eNoter

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Probability is the number of outcomes in event A divided by the total number of outcomes possible. Here, event A is drawing four cards (any 4). The total number of possible outcomes refers to the 52 total possible cards you could choose. Therefore, you create the fraction 4/52 and reduce or divide to get the probability. The probability can be expressed as 4/52, 0.076, or 7.6%.