﻿ Tree Diagram Worksheet | Problems & Solutions Tree Diagram Worksheet

Tree Diagram Worksheet
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1.
Use the tree diagram to find the probability of tossing a head first and then a tail when a coin is tossed twice.  a. 1 b. $\frac{1}{2}$ c. $\frac{1}{4}$ d. $\frac{1}{3}$

Solution:

The possible outcomes are (H, H), (H, T), (T, H) and (T, T).

Number of possible outcomes = 4.

The favorable outcome is (H, T).

Number of favorable outcomes = 1.

Probability (Head, Tail) = Number of favorable outcomesNumber of possible outcomes = 1 / 4.

2.
Tom can order a thick or thin crust pizza with 2 different toppings. The choices of toppings are mushroom and onions. Which diagram shows every possible combination of a pizza that Tom can order?

Solution: Draw a tree diagram to find the sample space.

The possible choices are as shown in Figure 4.

So, the tree diagram in Figure 4 shows the different choices that Tom has.

3.
Amy tossed a penny, a nickel, and a dime at the same time. Identify the tree diagram that shows all the possible outcomes.  a. Tree diagram 2 b. Tree diagram 4 c. Tree diagram 1 d. Tree diagram 3

Solution: Draw a tree diagram to find the sample space.

The possible outcomes are as shown in Tree Diagram 3.

So, Tree Diagram 3 shows all the possible outcomes.

4.
A store sells handbags in two colors: black and white. They are available in 2 different sizes: small and large. Which diagram shows every possible combination of the color and size of a bag that one can buy?  a. Tree diagram 3 b. Tree diagram 4 c. Tree diagram 1 d. Tree diagram 2

Solution: Draw a tree diagram to find the sample space.

The possible combinations are as shown in Tree diagram 2.

Tree diagram 2 shows all the possible choices available to buy a handbag.

5.
A bag contains 3 red and 5 white toys. Rose picked two toys one after the other. Which tree diagram shows all the possible combinations of toys that Rose picked?  a. Tree diagram 2 b. Tree diagram 1 c. Tree diagram 3 d. Tree diagram 4

Solution: Draw a tree diagram to find the sample space.

The possible outcomes are as shown in Tree Diagram 3.

Tree Diagram 3 shows all the possible outcomes.

6.
Sam needs to decide his snack. He can have milk or coffee followed by chocolate chips or peanut butter cookies. Which tree diagram shows the different choices that Sam has?  a. Tree diagram 4 b. Tree diagram 2 c. Tree diagram 3 d. Tree diagram 1

7.
There are two 'true or false' type of questions on a test paper. Pick the tree diagram that represents all the possible answers to these questions.  a. Tree diagram 1 b. Tree diagram 4 c. Tree diagram 2 d. Tree diagram 3

8.
A bag contains 3 yellow balls and 4 pink balls. Kay picked two balls one after the other. Which tree diagram shows all the possible outcomes?  a. Tree diagram 1 b. Tree diagram 2 c. Tree diagram 3 d. Tree diagram 4

9.
A tree diagram is useful in determining the __________ of a probability experiment. a. result b. possible outcomes c. event d. None of the above

Solution:

A tree diagram is useful in determining the possible outcomes of a probability experiment.

10.
Use the tree diagram to find the number of possible outcomes when a coin is tossed twice.  a. 2 b. 1 c. 4 d. None of the above

Solution:

The possible outcomes are HH, HT, TH, and TT.

So, the number of possible outcomes is 4.