Question

A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?

• A. \( \frac{5}{8} \)
• B. \( \frac{15}{28} \)
• C. \( \frac{3}{8} \)
• D. \( \frac{1}{2} \)

Hint:

Use combinations to calculate probabilities when dealing with random draws without replacement.

Answer 1

The Correct Option is B

The total number of balls is: \[ 5 + 3 = 8 \text{ balls}. \] The number of ways to draw 2 balls from 8 is: \[ \binom{8}{2} = \frac{8 \times 7}{2} = 28. \] The number of favorable outcomes (one red ball and one blue ball) is: \[ \binom{5}{1} \times \binom{3}{1} = 5 \times 3 = 15. \] Thus, the probability of drawing one red ball and one blue ball is: \[ \frac{15}{28}. \] The correct answer is: \[ \boxed{\frac{15}{28}}. \]