Toss a coin three times. How many ways can you get exactly two heads in the three tosses?

First toss: H or T

Second toss: H or T

Third toss: H or T

If we think about what happens after the first toss, we have H or T. For each of those outcomes, we get H or T on the second toss, so we now have 4 outcomes: HH, HT, TH, TT

With the third toss, each of our four outcomes could end with H or T, giving us 8 outcomes: HHH, HTH, THH, TTH, HHT, HTT, THT, TTT.

Out of these 8 possible outcomes, there are 3 outcomes with exactly 2 heads: HTH, THH, HHT.

We can also see the possibilies using a possibility tree, where the first (top) level represents the first toss, the second level, the second toss, and the third level, the third toss. The blue “paths” show the outcomes with exactly two Heads.