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## Probability using combinatorics

# Probability with counting outcomes

## Video transcript

Find the probability
of flipping exactly two heads on 3 coins. So to figure out this
probability, a good place to start is just to think about all
of the different possible ways that we can flip 3 coins. So we could get all tails. Tails, tails, tails. We could get tails,
tails, heads. We could get tails,
heads, tails. We could get tails,
heads, heads. We could get heads,
tails, tails. We could get heads,
tails, heads. We could get heads,
heads, tails. And then we could
get all heads. We could get all heads
over here. So there are 1, 2, 3, 4, 5,
6, 7, 8 possible outcomes. 8 possible outcomes. Now how many of the
outcomes involve flipping exactly 2 heads? Let's see, that's all tails. That's 1 head, 1 head. This has 2 heads right there. That's 1 head. This is 2 heads right
over there. Then this is 2 heads
right over here. And then this is 3 heads,
so that doesn't count. So there are 3 outcomes
with exactly 2 heads. So, let me spell
heads properly. 2 heads. So the probability of flipping
exactly 2 heads-- And the word exactly is important, because
if you didn't say exactly, then maybe 3 heads, when you
flip 2 heads, so we have to say exactly 2 heads. So you don't include
the situation where you get 3 heads. So the probability of flipping
exactly 2 heads is equal to the 3 outcomes with 2 heads
divided by the 8 possible outcomes, or 3/8. So it is equal to 3/8. And we are done.