Worksheet 9 2 math 7 answer key: Fill out & sign online | DocHub - Free Printable

Let's solve each problem step by step from Worksheet 9-2 – Math 7: Theoretical and Experimental Probability.

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Problem 1: Number Cube Rolled 24 Times

Given:
- A number cube (standard die) is rolled 24 times.
- Lands on 2 four times.
- Lands on 6 three times.

#### a. Experimental probability of landing on a 2

Experimental probability = (Number of times event occurred) / (Total number of trials)

$$
P(\text{landing on 2}) = \frac{4}{24} = \frac{1}{6}
$$

✔ Answer: $ \frac{1}{6} $

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#### b. Experimental probability of *not* landing on a 6

First, find how many times it did not land on 6:

- Total rolls = 24
- Landed on 6 = 3 times
- So, did not land on 6 = $ 24 - 3 = 21 $

$$
P(\text{not landing on 6}) = \frac{21}{24} = \frac{7}{8}
$$

✔ Answer: $ \frac{7}{8} $

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#### c. Compare experimental probability in part a to theoretical probability

Theoretical probability of rolling a 2 on a fair six-sided die:

$$
P(\text{rolling a 2}) = \frac{1}{6}
$$

Experimental probability from part a: $ \frac{1}{6} $

✔ They are equal.

> ✔ Explanation: In this case, the experimental result matches the theoretical expectation exactly.

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#### d. Compare experimental probability in part b to theoretical probability

Theoretical probability of NOT landing on 6:

- P(6) = $ \frac{1}{6} $
- So, P(not 6) = $ 1 - \frac{1}{6} = \frac{5}{6} $

Experimental probability from part b: $ \frac{7}{8} = 0.875 $

Compare:
- $ \frac{5}{6} \approx 0.833 $
- $ \frac{7}{8} = 0.875 $

So, the experimental probability ($ \frac{7}{8} $) is slightly higher than the theoretical ($ \frac{5}{6} $).

✔ Answer: The experimental probability ($ \frac{7}{8} $) is greater than the theoretical probability ($ \frac{5}{6} $), which may be due to random variation in a small sample size.

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Problem 2: ENTERTAINMENT Survey

| Type of Entertainment | Percent |
|-----------------------------|--------|
| Playing Interactive Games | 48% |
| Reading Books | 22% |
| Renting Movies | 10% |
| Going to Movie Theaters | 10% |
| Surfing the Internet | 9% |
| Watching Television | 1% |

#### a. Probability that someone considered reading books OR surfing the Internet as best entertainment

Add percentages:
- Reading Books: 22%
- Surfing Internet: 9%

$$
P(\text{Books or Internet}) = 22\% + 9\% = 31\% = \frac{31}{100}
$$

✔ Answer: $ \frac{31}{100} $

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#### b. Out of 500 people surveyed, how many would you expect to consider reading books or surfing the Internet?

Use the probability from part a:

$$
\text{Expected number} = 500 \times \frac{31}{100} = 155
$$

✔ Answer: 155 people

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#### c. Out of 300 people, is it reasonable to expect 30 considered watching TV as best value? Why or why not?

From table: Watching TV = 1%

So expected number out of 300:
$$
300 \times 0.01 = 3
$$

But we’re asked if 30 is reasonable.

- Expected = 3
- But they say 30 → That’s 10 times higher than expected.

✔ Answer: No, it is not reasonable.
Only 1% of people chose watching TV, so we'd expect only about 3 out of 300, not 30. Expecting 30 is unrealistic based on the data.

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Problem 3: Spinner with Four Colors

Spun 100 times:

| Section | Frequency |
|---------|-----------|
| Blue | 14 |
| Green | 10 |
| Yellow | 8 |
| Red | 68 |

#### a. Experimental probability of landing on green

$$
P(\text{green}) = \frac{10}{100} = \frac{1}{10}
$$

✔ Answer: $ \frac{1}{10} $

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#### b. Experimental probability of landing on red

$$
P(\text{red}) = \frac{68}{100} = \frac{17}{25}
$$

✔ Answer: $ \frac{17}{25} $

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#### c. If spun 50 more times, how many times would you expect to land on blue?

From previous spins:
- Blue occurred 14 times out of 100 → experimental probability = $ \frac{14}{100} = 0.14 $

Now, for 50 more spins:

$$
\text{Expected blue} = 50 \times 0.14 = 7
$$

✔ Answer: 7 times

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✔ Final Answers Summary:

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#### Problem 1
a. $ \frac{1}{6} $
b. $ \frac{7}{8} $
c. Experimental = Theoretical = $ \frac{1}{6} $ → Match
d. Experimental ($ \frac{7}{8} $) > Theoretical ($ \frac{5}{6} $) → Slight difference due to chance

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#### Problem 2
a. $ \frac{31}{100} $
b. 155 people
c. No, because only 1% prefer TV → expect ~3, not 30

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#### Problem 3
a. $ \frac{1}{10} $
b. $ \frac{17}{25} $
c. 7 times

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