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A fair coin is tossed 3 times. What is the probability
that the coin landed tails up exactly twice?
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For this question, our desired outcome
is to toss 2 tails and 1 head. The number of possible desired outcomes
is therefore the number of different ways in which we can toss two tails
and one head in three tosses. We can draw these possibilities as follows:
Our number of possible outcomes is the
number of different outcomes that could result from three tosses. Since
each of the three tosses can be either heads or tails, the number of possible
outcomes is equivalent to 2 
2
2 = 8. To be precise, we can draw
out our 8 possible outcomes:
Since we have three different outcomes of two
tails, and eight different outcomes in total, the probability of tossing
exactly two tails is 
. This
probability fraction can also be obtained by calculating
out the probabilities for each individual toss.
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