Question

Sara selects two cards at random from a standard deck of fifty-two cards. Which of the following could be used to calculate the probability that she will select two numbered cards if she does not replace the first card before selecting the second? Note: For this problem, face cards and aces are not numbered cards.

Answer 1

.
thirty-six divided by fifty-two times thirty-five divided by fifty-one
thirty-six divided by fifty-two times thirty-five divided by fifty-two
thirty-six divided by fifty-two times thirty-six divided by fifty-two
thirty-six divided by fifty-two times thirty-six divided by fifty-one

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Answer 2

Let the initial quantity of numbered cards be n cards. The probability of the first selection being a numbered card is n/52.
If a numbered card is selected on the first selection, there are n - 1 numbered cards remaining and 51 cards are left in the pack. Therefore the probability of the second selection being a numbered card is (n - 1)/51.
The required probability is therefore given by:
\[\large \frac{n}{52} \times \frac {n-1}{51}\]