An urn contains 2 yellow, 4 green, 1 white and 3 red marbles. If two marbles are drawn at random from the urn, then what is the probability that both are green?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{2}{15}\)
Two marbles drawn together form a selection, so both the favourable and the total cases are counted with combinations.
Total marbles: \(2+4+1+3=10\); ways to draw 2: \(\displaystyle ^{10}C_2=\frac{10\times9}{2}=45\)
Ways to draw 2 of the 4 green marbles: \(\displaystyle ^{4}C_2=\frac{4\times3}{2}=6\)
Probability \(\displaystyle =\frac{6}{45}=\frac{2}{15}\)