A jar contains 3 green marbles and 2 red marbles. If two marbles are selected at random on… — GMAT

A jar contains $3$ green marbles and $2$ red marbles. If two marbles are selected at random one after another without replacement, what is the probability that both selected marbles are green?

Answer: 0.3

Answer

The probability that both selected marbles are green is

0.3

Because selection is done without replacement, the outcome of the first draw changes the composition of the jar for the second draw. The probability of selecting a green marble first is

3/5

. With one green marble removed,

2

green marbles remain among

4

total marbles, so the probability of selecting green on the second draw is

2/4

. Multiplying these sequential probabilities gives

(3/5) \times (2/4) = 6/20 = 0.3

Step-by-Step Solution

Calculate the probability of drawing a green marble on the first selection.

P(\text{First Green}) = \frac{3}{5}

There are

3

green marbles out of

5

total marbles in the jar.

Calculate the conditional probability of drawing a green marble on the second selection.

P(\text{Second Green} \mid \text{First Green}) = \frac{2}{4} = \frac{1}{2}

Because the first marble was not replaced,

2

green marbles remain out of a total of

4

remaining marbles.

Multiply the probabilities of the dependent sequential events.

P(\text{Both Green}) = \frac{3}{5} \times \frac{1}{2} = \frac{3}{10} = 0.3

The probability of both dependent events occurring is the product of the first event's probability and the conditional probability of the second event.

Key Concept

Probability of Dependent Events Without Replacement

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