Question

A bag contains 6 white and 4 black ball. Two balls are drawn at random. Then the probability of getting balls of the same colour is ___.

• A. \(\frac{8}{15}\)
• B. \(\frac{6}{15}\)
• C. \(\frac{6}{13}\)
• D. \(\frac{7}{15}\)

Answer 1

The Correct Option is D

The problem requires finding the probability of drawing two balls of the same color from a bag containing 6 white and 4 black balls.

First, calculate the total number of ways to draw two balls from the bag:

\( \text{Total ways} = \binom{10}{2} = \frac{10 \times 9}{2 \times 1} = 45 \)

Next, calculate the number of ways to draw two white balls:

\( \text{White balls ways} = \binom{6}{2} = \frac{6 \times 5}{2 \times 1} = 15 \)

Then, calculate the number of ways to draw two black balls:

\( \text{Black balls ways} = \binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6 \)

The total number of ways to draw two balls of the same color is the sum of the above two:

\( 15 + 6 = 21 \)

Therefore, the probability of drawing two balls of the same color is:

\( P(\text{same color}) = \frac{21}{45} = \frac{7}{15} \)

The probability of drawing two balls of the same color is \(\frac{7}{15}\).