Multiple choice

Directions: Compare Quantity A and Quantity B using additional information centered above the two quantities if such information is given. Select one of the four answer choices. Four cards are drawn from a pack of 52 playing cards. Quantity A Quantity B Probability of getting all the four cards of same suit. 44/4165

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both the quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Probability of 4 cards of the same suit: Choose 1 suit (4 ways), then choose 4 cards from 13 (C(13,4)). Total ways = C(52,4). P = (4 * C(13,4)) / C(52,4) = (4 * 715) / 270725 = 2860 / 270725 = 44 / 4165. Both quantities are equal.

AI explanation

We calculate Quantity A using combinations by finding the probability of drawing 4 cards of the same suit. There are 4 suits, so the number of ways to draw 4 cards of one suit is 4 multiplied by 13 factorial divided by the product of 4 factorial and 9 factorial, which equals 2860. The total ways to draw 4 cards from 52 is 52 factorial divided by the product of 4 factorial and 48 factorial, equaling 270725. The probability is 2860 divided by 270725, which simplifies by dividing the numerator by 5 and the denominator by 5 to 572 divided by 54145, and dividing both by 13 results in 44 divided by 4165. Both quantities are equal.

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