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Probability of Selecting Certain Marbles from a Bag

A box contains 4 marbles: 2 red, one blue and one green. Two marbles will be selected at random. Find the probability of selecting each of the following.

A) with replacement B) without replacement

i A red marble and then a blue marble

ii Two blue marbles

iii No red marbles

iv No green marbles.

Solution Preview

A) with replacement

i A red marble and then a blue marble
probability of one red marble is 0.5 (or 50%)
probability of a blue is 0.25
Therefore, the probability in that order is 0.5 x 0.25 = 0.125

ii Two blue marbles
probability of one blue is 0.25
probability of another blue is the same
therefore, the probability of two blues is 0.25 x 0.25 = 0.0625

iii No red marbles
probability of either a blue or a green is 0.50 (2 out of 4)
probability of ...

Solution Summary

354-word solution with calculations showing how to work out the probability of selecting certain colored marbles from a mixed bag both with and without replacement.