# Worksheet: Counting Outcomes Using Tree Diagrams

Q1:

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.

• A14 out of 56
• B49 out of 56
• C8 out of 56
• D7 out of 56

Q2:

Using the Fundamental Counting Principle, determine the total number of outcomes of tossing 3 quarters and 3 pennies.

Q3:

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.

Q4:

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?

Q5:

Use the Fundamental Counting Principle to find the total number of outcomes of rolling 4 number cubes and tossing 2 coins.

Q6:

Use the Fundamental Counting Principle to find the total number of outcomes of tossing 11 coins.

Q7:

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

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

Q10:

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.

• A25 out of 40
• B27 out of 45
• C30 out of 45
• D15 out of 45
• E12 out of 40

Q11:

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

• A
• B
• C
• D
• E