Lesson: Counting Outcomes Using Tree Diagrams

In this lesson, we will learn how to find all possible outcomes for an experiment using tree diagrams and the Fundamental Counting Principle.

Sample Question Videos

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Worksheet: Counting Outcomes Using Tree Diagrams • 11 Questions • 4 Videos

Q1:

Use the fundamental counting principle to determine the total number of outcomes of picking out an outfit from 4 shirts, 8 pairs of pants, and 2 jackets.

Q2:

Suppose there are 9 sheep whose fur may be only one of two colours, white or brown. Using the tree diagram, determine the total number of possible sheep-colour choices.

Q3:

Two spinners are spun. The first spinner is numbered from 1 to 7, and the second spinner is numbered from 1 to 8. Using a tree diagram, determine the probability of both spins being the same number.

Q4:

Using the fundamental counting principle, determine the total number of outcomes of tossing 3 quarters and 3 pennies.

Q5:

In how many ways can a shirt and a hat be chosen, given 20 shirts and 13 hats to choose from?

Q6:

Use the fundamental counting principle to find the total number of outcomes of rolling 4 number cubes and tossing 2 coins.

Q7:

Use the fundamental counting principle to find the total number of outcomes of tossing 11 coins.

Q8:

Use the fundamental counting principle to determine the total number of outcomes of choosing, with the possibility of repetition, a password that consists of three letters and three numbers from 1 to 7.

Q9:

Suppose two spinners are spun. The first has 5 equal sectors numbered from 1 to 5, and the second has 9 equal sectors numbered from 1 to 9. Using a tree diagram or otherwise, find the probability that both spinners stop at odd numbers.

Q10:

An experiment consists of flipping a coin and rolling a six sided die once, then observing the upper faces of both. Event 𝐴 is when the coin lands tail side up and the die lands with an even number facing up. Event 𝐵 is when the coin lands head side up and the die lands with an odd number facing up. Determine the range of event 𝐶 , which is the occurrence of events 𝐴 and 𝐵 .

Q11:

A bag contains 3 balls numbered from 1 to 3. In an experiment, a ball is selected at random from the bag, replaced, and then another ball is selected. How many possible outcomes are there?

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