You spin a spinner divied into thirds and labled a, b, c, and you flip a coin.

use a tree diagram to answer the question.
How many outcomes show heads and b?

To answer the question, let's create a tree diagram considering the two events: flipping a coin and spinning a spinner.

Start by drawing two branches from the beginning, one labeled "Heads" and the other labeled "Tails." Then draw three branches from each "Heads" and "Tails" branch, representing the three sections on the spinner: a, b, and c.

The tree diagram should look something like this:

/
H /\
/ \
B C
/ \
a b
/ \
T C
/ \
a b

Now, to determine the number of outcomes that show heads and b, we need to count the number of branches that lead to the "Heads" and "b" combination. In this case, there is only one branch that meets this condition: the branch that goes from "Heads" to "b."

Therefore, there is only one outcome that shows heads and b.

To answer this question using a tree diagram, we can start by drawing a tree with two branches representing the two possible outcomes of flipping a coin: heads (H) and tails (T). Then, on each branch, we can draw three additional branches representing the three possible outcomes of spinning the spinner: a, b, and c.

Here's the tree diagram:

H (heads)
/ \
a b
/ | \ / | \
H T H T H T
/ | | | | |
a b c a b c

Now, we can count the number of outcomes that show heads and b. Looking at the diagram, there are two outcomes that satisfy both conditions: H and b, and T and b.

Therefore, there are two outcomes that show heads and b.