Question

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red,...

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability that both marbles are white.

Solution :

Number of white marbles = 3

Number of green marbles = 2

Number of red marbles = 2

Number of blue marbles = 1

Total number of marbles = 3+2+2+1 = 8

Two marbles are drawn without replacement.

We have to find the probability that both marbles are white.

Probability that first drwan marble is white = number of white marbles/total number of marbles

Probability that first drwan marble is white = 3/8

Now, since marbles are drawn without replacement and one white marble is already drawn, therefore now we have total 7 marbles in which there are two white marbles.

Probability that second drawn marble is white = 2/7

Using the multiplication theorem of probability we shall get the probability that both marbles are white.

Hence, probability that both marbles are white = (3/8) × (2/7) = 3/28

The probability that both marbles are white is 3/28.

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