How do you make a tree diagram to show the sample space after tossing four pennies?

Answer 1

You start with a point along the left edge of a page, halfway down. Form that point you have two line segments representing the outcomes of the first toss: a line going upwards (indicating Heads, H) and the other going downwards (indicating Tails, T). The letters H and T are written at the end of the line segments with the probability of each outcome written alongside the line. From the point marked H you repeat the two branches, representing the outcomes of the second toss and do the same from the T. From the two Hs and two Ts, repeat for the outcome of the third toss and then for the fourth. You should end up with a tree, going left to right, and ending with 16 (=2*2*2*2) outcomes.

It is a good idea to be systematics about drawing a tree diagram: always have the same outcome for the lines going up. That way you can be sure that you make mistakes.