A box contains 1 white 3 blue and 4 silver marbles Two marbl

A box contains 1 white, 3 blue and 4 silver marbles. Two marbles are randomly selected without replacement. Find the indicated probabilities.

A) what is the probability both marbles are blue?

B) what is the probability both marbles are the same color?

C) what is the probability neither marble is blue?

D) what is the probability that the 1st one is silver and the 2nd one is blue?

Solution

There are 8 marbles. Thus, there are 8C2 = 28 ways to get any 2 balls.

a)

There are 3C2 = 3 ways to get 2 blue balls.

Thus,

P(both blue) = 3/28 or 0.107142857 [answer]

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b)

There are 3C2 ways to get both blue, 4C2 ways to get both red.

Thus,

P(same color) = (3C2 + 4C2)/28 = 0.321428571 [answer]

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c)

There are 5C2 ways to get two non-blues.

P(neither blue) = (5C2) / (8C2) = 0.357142857 [answer]

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d)

There are 4*3 = 12 ways to get a silver and blue in that order.

There are 8P2 = 56 ways to get 2 balls if order is relevant.

Thus,

P(silver then blue) = 12/56 = 0.214285714 [answer]