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
Total number of marbles in urn = 10
Number of selecting 2 marbles = \(\frac{10 × 9 × 8! }{8! × 2 × 1 }\) = 45
number of green marbles = 4
Number of selecting 2 green marbles = \(\frac{4 × 3 × 2! }{2! × 2 × 1 }\) = 6
Probability that both drawn marbles are green = \(\frac{ 4C2 }{ 10C2 }\)
= \(\frac{ 6 }{ 45 }\)
= \(\frac{ 2 }{ 15 }\)
The correct answer is option (2) : $\frac{2}{15}$