Instructions

Study the given information carefully and answer the questions that follow:
An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.

Question 107

If three marbles are picked at random, what is the probability that two are blue and one is yellow ?

Solution

Total number of marbles in the urn = 15

P(S) = Total possible outcomes

= Selecting 3 marbles at random out of 15

=> $$P(S) = ^{15} C_3 = \frac{15 \times 14 \times 13}{1 \times 2 \times 3}$$

= $$455$$

P(E) = Favorable outcomes

= Selecting 2 blue and 1 yellow marble.

=> $$P(E) =C^6_2 \times C^4_1$$

= $$\frac{6 \times 5}{1 \times 2} \times 4$$

= $$60$$

$$\therefore$$ Required probability = $$\frac{P(E)}{P(S)}$$

= $$\frac{60}{455} = \frac{12}{91}$$

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