We included **HMH Into Math Grade 7 Answer Key PDF** **Module 15 Understand and Apply Theoretical Probability **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 15 Answer Key Understand and Apply Theoretical Probability

**Analyzing Rock-Paper-Scissors**

Destiny and Mateo are in the semi-finals of a Rock-Paper- Scissors tournament. Rock-Paper-Scissors is a game for two players, using the three hand signals shown. Players count, “1, 2, 3, go!” and then each player makes a hand signal for rock, paper, or scissors. Each player has an equal chance of winning.

Rock (R) beats scissors (S); Scissors (S) beat paper (P); Paper (P) beats rock (R)

A. The table shows the results of Destiny and Mateo’s match. Complete the table by filling in the missing entries.

Answer:

B. Complete the statements. Write each experimental probability as a fraction and as a decimal.

- Destiny(D) chose Rock __________ times. P(DR) = or __________
- Mateo(M) chose Rock __________ times. P(MR) = or __________
- Destiny chose Paper __________ times. P(DP) = or __________
- Mateo chose Paper __________ times. P(MP) = or __________

Answer:

- Destiny(D) chose Rock 2 times. P(DR) = 2/10 or 0.2
- Mateo(M) chose Rock 5 times. P(MR) = 5/10 or 0.5
- Destiny chose Paper 4 times. P(DP) = 4/10 or 0.4
- Mateo chose Paper 3 times. P(MP) = 3/10 or 0.3

**Turn and Talk**

Calculate each player’s experimental probability of choosing scissors. Explain your method of calculation.

Answer: The experimental probability of choosing scissors for each player is 3/10 for Destiny and 2/10 for Mateo.

**Are You Ready?**

Complete these problems to review prior concepts and skills you will need for this module.

**More Likely, Less Likely, Equally Likely**

Use the spinner to answer the questions.

Question 1.

Which event is more likely than spinning a 1?

Answer:

Total = 8

The event is more likely than spinning a 1 is 3/8.

Question 2.

Which event is less likely than spinning a 1?

Answer:

Total = 8

The event is less likely than spinning a 1 is 1/8

Question 3.

Which event is equally likely as spinning a 1?

Answer:

Total = 8

The event is equally likely than spinning a 1 is 2/8 or 1/4.

**Experimental Probability**

The number of each type of bar in a variety pack of granola bars can vary. The table shows the number of peanut butter bars in a random sample of 300 variety packs. Use this information for Problems 4-6.

Question 4.

What is the experimental probability that a variety pack will have exactly 3 peanut butter bars?

Answer:

Total frequency = 300

A variety pack will have exactly 3 peanut butter bars = 75

The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.

Experimental Probability = 75/300

Question 5.

What is the experimental probability that a variety pack will have at most 4 peanut butter bars?

Answer:

Total frequency = 300

A variety pack will have at most 4 peanut butter bars = 11 + 29 + 60 + 75 + 71 = 246

The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.

Experimental Probability = 246/300

Question 6.

Esme buys 15 variety packs. How many packs can she expect to have more than 2 peanut butter bars? Explain your reasoning.

Answer:

Esme buys 15 variety packs.

15 variety packs have 6 peanut butter bars.