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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 𝐴 is when the coin lands tail side up and the die lands with an even number facing up. Event 𝐡 is when the coin lands head side up and the die lands with an odd number facing up. Determine the range of event 𝐢 , which is the occurrence of events 𝐴 and 𝐡 .

  • A 𝐢 = { ( , 1 ) , ( , 3 ) , ( , 5 ) , ( , 2 ) , ( , 4 ) , ( , 6 ) } H H H T T T
  • B 𝐢 = { ( , 2 ) , ( , 4 ) , ( , 6 ) , ( , 1 ) , ( , 3 ) , ( , 5 ) } H H H T T T
  • C 𝐢 = { ( , 1 ) , ( , 2 ) , ( , 3 ) , ( , 4 ) , ( , 5 ) , ( , 6 ) , ( , 1 ) , ( , 2 ) , ( , 3 ) , ( , 4 ) , ( , 5 ) , ( , 6 ) } H H H H H H T T T T T T
  • D 𝐢 = βˆ…
  • E 𝐢 = { ( , 2 ) , ( , 3 ) , ( , 5 ) , ( , 6 ) , ( , 2 ) , ( , 3 ) , ( , 5 ) , ( , 6 ) } H H H H T T T T