Question

A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is

• A. \( \frac{3}{16} \)
• B. \( \frac{45}{236} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{3}{4} \)

Hint:

When calculating probabilities without replacement, adjust the total number of possible outcomes after each selection.

Answer 1

The Correct Option is B

- The total number of balls is \( 15 + 45 = 60 \).
- The probability of selecting a blue ball first is \( \frac{15}{60} = \frac{1}{4} \).
- After removing one blue ball, the total number of balls becomes \( 59 \), and the number of black balls is \( 45 \). Thus, the probability of selecting a black ball after selecting a blue ball is \( \frac{45}{59} \).
Therefore, the probability of selecting a blue ball first and a black ball second is: \[ P(\text{blue first, black second}) = \frac{15}{60} \times \frac{45}{59} = \frac{45}{236} \] Thus, the correct answer is (B).