Question
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Answer: Option A
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = $$\frac{{{}^3{C_3}}}{{{}^{15}{C_3}}}$$
$$\eqalign{
& = \frac{{1 \times 3 \times 2 \times 1}}{{15 \times 14 \times 13}} \cr
& = \frac{6}{{2730}} \cr
& = \frac{1}{{455}} \cr} $$
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Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = $$\frac{{{}^3{C_3}}}{{{}^{15}{C_3}}}$$
$$\eqalign{
& = \frac{{1 \times 3 \times 2 \times 1}}{{15 \times 14 \times 13}} \cr
& = \frac{6}{{2730}} \cr
& = \frac{1}{{455}} \cr} $$
Was this answer helpful ?
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