Question

For which of these situations is a tree diagram a good method to show all possible outcomes in the sample space? (Select the three correct answers.)
A. Counting the total number of cars parked in a parking lot.
B. Choosing an outfit from a selection of three shirts and two pants.
C. Flipping a coin and then rolling a standard number cube.
D. Measuring the current height of a single growing plant.
E. Picking one student from a large classroom of twenty-five.
F. Spinning a spinner with three different sections two times.

Answer 1

B, C, and F.

- B (3 shirts × 2 pants = 6 outfit combinations) — two-stage choice, easy to list with a tree.
- C (coin then number cube = 2 × 6 = 12 outcomes) — sequential events, tree shows all pairs.
- F (spinner with 3 sections spun twice = 3 × 3 = 9 outcomes) — repeated stages, tree lists all ordered pairs.

A, D, and E are not good fits (single large count or continuous measurement rather than a small sequence of discrete stages).