Multiple choice

A deck of 8 cards contains 3 red cards, 3 black cards, and 2 blue cards. A player randomly picks 2 cards. Quantity A Probability that both selected cards are the same color Quantity B Probability that the selected cards are of different colors

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total ways to pick 2 cards = 8C2 = 28. Same color: (3C2 + 3C2 + 2C2) = 3 + 3 + 1 = 7. P(Same) = 7/28 = 1/4. Different color: 1 - 1/4 = 3/4. Quantity B (3/4) is greater than Quantity A (1/4).

AI explanation

The probability of selecting two cards of the same color is the sum of choosing two red, two black, or two blue cards: (3C2 + 3C2 + 2C2) / 8C2 = (3 + 3 + 1) / 28 = 7/28 = 1/4. The probability of selecting two cards of different colors is 1 - 1/4 = 3/4. Since 3/4 is greater than 1/4, Quantity B is greater.

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