Question

Three cards are drawn simultaneously from a well-shuffled pack of 52 cards. What is the probability that two of them are even-numbered cards, and one is an odd-numbered card?

(a) 1​/34
(b) 1/26​
(c) 1/17​
(d) 1/13​

Answer 1

The probability is 1/34 that two cards drawn from a shuffled deck of 52 cards are even-numbered and one card is odd-numbered. The correct option is (a) 1​/34.

Step-by-step explanation:

To find the probability that two cards are even-numbered and one card is odd-numbered, we need to determine the number of favorable outcomes and the total number of possible outcomes.

There are 26 even-numbered cards (2, 4, 6, ..., 52) and 26 odd-numbered cards (1, 3, 5, ..., 51) in a deck of 52 cards.

The number of ways to select 2 even-numbered cards from 26 is C(26, 2) = 325. The number of ways to select 1 odd-numbered card from 26 is C(26, 1) = 26. The total number of ways to draw 3 cards from a deck of 52 cards is C(52, 3) = 22,100.

Therefore, the probability is (325 * 26) / 22,100 = 1 / 34.