All the Outcomes of Two Spins: Tables and Tree Diagrams

0:00If we spin this spinner twice, how likely is the same number both times?

0:06The spinner has 3 equal parts, numbered 1, 2 and 3.

0:12One outcome is a 1 on the first spin, then a 3 on the second.

0:20To list every outcome, put the first spin down the side and the second across the top.

0:26Each box is one outcome, like 1 then 3.

0:313 rows of 3 boxes make 9 outcomes.

0:35A tree diagram shows the same outcomes, starting with 3 branches for the first spin.

0:41Each of those splits into 3 more branches for the second spin.

0:46Each path from left to right is one outcome, like 1 then 3.

0:52There are 9 paths, so 9 outcomes, just like the table.

0:571 then 3 and 3 then 1 are different outcomes, so we count both.

1:03All 9 outcomes are equally likely, and 3 of them have the same number twice.

1:10So the probability of the same number twice is 3 out of 9, or one third.

1:16A table or a tree diagram shows every outcome of two events.