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This problem trains for: AMC-8, SAT-I, SAT-II, AMC-10.

In a bag there are 5 white marbles and 11 red marbles. Someone draws blindfolded 3 marbles out. What is the probability that exactly 2 of the marbles are red?

Solution 1:

Use the rules for adding and multiplying probabilities of events to obtain the probability of a combined event:

The favorable events are: RRW, RWR and WRR. The probabilities for each to happen are:

The probability for any one of these events to happen is:

Solution 2:

Count the number of favorable cases and the total number of cases and divide: