If only cards could talk!
You have 4 playing cards in your hand. 2 of them are Kings and 2 of them are Queens. You told one of your friends to choose 2 cards randomly from these 4 cards. Let the probability that the chosen cards consist of a King and a Queen be where and are coprime positive integers. What is the value of ?
The answer is 5.
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1 solution
Let's assume he's choosing one card at a time randomly. (This is similar to the situation where he picks 2 cards at once.)
For case-1, we'll assume that the first chosen card is a King. Now, the remaining 3 cards comprise of 2 Queens and 1 King. Hence, the probability that he'd get a Queen for the second pick is 3 2 .
For case-2, we'll assume that the first card is a Queen. So, the remaining cards consist of 2 Kings and 1 Queen. Therefore, the probability of getting a King next is also 3 2 .
Finally, case-1 and case-2 are equally likely as the number of Kings and Queens are equal initially. As a result, the probability of getting one King and one Queen is 3 2 .