KA-0068Tree diagrams
4 points, difficulty 2 of 3Level 3–4about 75sA coin is tossed three times. In how many of the possible outcomes are there exactly two heads?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
List all eight outcomes in order.
2The strategy
Three tosses give eight outcomes. Write them in a fixed order so none is missed, then count the ones with exactly two heads — not two or more.
3The full solution
The eight are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Exactly two heads: HHT, HTH, THH. That is 3.
Solution
The reliable way
Write out all eight outcomes systematically: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Now pick the ones with exactly two heads: HHT, HTH, THH — three of them. HHH has three heads, so it does not count. The transferable idea: exactly means exactly, and a full list in a fixed order is the safest way to obey it.
The elegant way
Two heads means choosing which one of the three tosses is the tail, and there are 3 ways to do that.
Why this is on the test: Reading exactly as at least is a comprehension error that turns a correct method into a wrong answer.