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 109

If two marbles are picked at random, what is the probability that either both are red or both are green ?

Solution

Total number of marbles in the urn = 15

P(S) = Total possible outcomes

= Selecting 2 marbles at random out of 15

=> $$P(S) = C^{15}_2 = \frac{15 \times 14}{1 \times 2}$$

= $$105$$

P(E) = Favorable outcomes

= Selecting 2 green or 2 red marbles.

=> $$P(E) = C^2_2 + C^3_2$$

= $$1 + \frac{3 \times 2}{1 \times 2}$$

= $$4$$

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

= $$\frac{4}{105}$$

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