A bag contains 6 white and 4 black balls. Two balls are drawn at random. Then the probability of getting balls of the same colour is ____.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{7}{15}\)
The two balls are drawn together, so order does not matter and the ways are counted as combinations. “Same colour” means both white or both black.
All ways of drawing 2 of the 10 balls: \(^{10}C_2=45\)
Both white, 2 chosen from the 6 white balls: \(^{6}C_2=15\)
Both black, 2 chosen from the 4 black balls: \(^{4}C_2=6\)
Favourable ways (both white or both black) over all ways: \(\displaystyle\frac{15+6}{45}=\frac{21}{45}=\frac{7}{15}\)