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 ______.
1. \(\dfrac{45}{236}\)
2. \(\dfrac{1}{4}\)
3. \(\dfrac{3}{16}\)
4. \(\dfrac{3}{4}\)

Answer 1

Correct Answer - Option 1 : \(\dfrac{45}{236}\)

Concept:

\(P(E) = \frac{Number~of~favorable~outcomes}{Total~number~of~outcomes}\)

Calculation:

Given:

Number of blue balls = 15, Number of black balls = 45

Total number of balls = 15 + 45 = 60 balls

Balls are drawn from the box at random without replacement.

The probability of drawing first blue ball and second black ball is;

\(P(E)= \frac{{{15_{{C_1}}}}}{{{60_{{C_1}}}}}\times \frac{{{45_{{C_1}}}}}{{{59_{{C_1}}}}}\)

\(P(E) = \frac{15\times45}{60\times59}\)

\(P(E) = \frac{45}{236}\)