Question

lona tossed a coin twice. she made a tree diagram to show the possible outcomes. which tree diagram shows the sample space for two tosses of a coin?

Explanation:

Step1: Recall coin toss sample space

When tossing a coin twice, the first toss has 2 outcomes: H (heads) or T (tails). For each of these, the second toss also has 2 outcomes. So the sample space should be: HH, HT, TH, TT.

Step2: Analyze tree diagrams

• First tree diagram: Let's check the branches. If the first level is T and H, then the second level for T: if one branch is missing (or incorrect), and for H: branches H and H? No, that's wrong. The second toss after H should be T and H.
• Second tree diagram: Root (first toss) has T and H. Then each of those (T and H) branches into T and H. So the paths are: T->T, T->H, H->T, H->H. Which matches the sample space for two coin tosses (TT, TH, HT, HH). So this is correct.

Answer:

The second tree diagram (the one with root, then T and H, then each of those branches into T and H)