Worksheet 9 2 Math 7 Answer Key - Fill Online, Printable, Fillable ... - Free Printable

Let’s solve each problem step by step.

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Problem 5: Number Cube Rolled 120 Times

We’re told:
- Total rolls = 120
- Sixes rolled = 25

a. Experimental probability of rolling a six

Experimental probability = (number of times event happened) ÷ (total number of trials)

→ So, 25 ÷ 120

Simplify that fraction:

Divide numerator and denominator by 5 → 5/24

So experimental probability = 5/24

(You can also write as decimal ≈ 0.2083, but fraction is fine unless asked otherwise.)

b. Theoretical probability of not landing on a 6

A standard cube has 6 sides: 1, 2, 3, 4, 5, 6

Probability of NOT rolling a 6 = probability of rolling 1, 2, 3, 4, or 5 → that’s 5 outcomes out of 6

→ So theoretical probability = 5/6

c. Compare experimental vs theoretical for “not landing on 6”

First, find experimental probability of NOT rolling a 6:

Total rolls = 120
Sixes = 25 → so non-sixes = 120 - 25 = 95

Experimental P(not 6) = 95 / 120

Simplify: divide numerator and denominator by 5 → 19/24

Theoretical P(not 6) = 5/6 = 20/24 (to compare easily)

So:

- Experimental: 19/24
- Theoretical: 20/24

They are close — experimental is just a little lower than theoretical. That makes sense because in real experiments, results don’t always match theory exactly, especially with only 120 trials.

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Problem 6: Survey Results Table

Table shows:

| Type of Entertainment | Percent |
|------------------------|---------|
| Playing Board Games | 46 |
| Reading Books | 25 |
| Seeing Movies | 10 |
| Going to Sports Events | 10 |
| Surfing the Internet | 9 |
| Watching Television | ? |

Wait — let’s check if percents add up to 100.

Add known percents:
46 + 25 = 71
71 + 10 = 81
81 + 10 = 91
91 + 9 = 100

Oh! So watching television must be 0%? That doesn’t make sense. Wait — maybe I misread.

Actually, looking again — the table says “Percent” but doesn’t say total is 100. But usually survey percentages should add to 100. Let me double-check addition:

Playing Board Games: 46
Reading Books: 25 → total so far: 71
Seeing Movies: 10 → 81
Going to Sports Events: 10 → 91
Surfing the Internet: 9 → 100
Watching Television: ???

If all others add to 100, then Watching Television must be 0? That seems odd. Maybe it's a typo? Or perhaps the table includes "Watching Television" as part of another category? But no — it’s listed separately.

Wait — actually, let’s re-add carefully:

46 (Board Games)
+25 (Books) = 71
+10 (Movies) = 81
+10 (Sports) = 91
+9 (Internet) = 100
Then Television is left — but 100 already reached. So either:

- There’s an error in the table, OR
- “Watching Television” is included in one of the other categories? Unlikely.

But since the question asks about probability based on this data, we’ll assume the percents given are correct and sum to 100 — meaning Watching Television is 0%. That seems strange, but mathematically, we go with what’s given.

Alternatively — maybe I missed something. Let me look again at the original image description.

In the user’s text, under Problem 6, the table lists:

Playing Board Games — 46
Reading Books — 25
Seeing Movies — 10
Going to Sports Events — 10
Surfing the Internet — 9
Watching Television — [blank?]

Wait — in the original problem statement you provided, it says:

> Real Experimental Value
> Type of Entertainment | Percent
> Playing Board Games | 46
> Reading Books | 25
> Seeing Movies | 10
> Going to Sports Events | 10
> Surfing the Internet | 9
> Watching Television | ?

And then questions follow.

But when we add 46+25+10+10+9 = 100. So Watching Television must be 0%. Perhaps it’s a trick, or maybe it’s meant to be calculated differently.

Actually — wait! In many such problems, sometimes the last value is missing and you have to calculate it to make total 100. But here, adding the five gives 100, so sixth must be 0.

I think we proceed assuming Watching Television = 0%, even though it’s unusual.

Now answer the questions:

a. Probability that someone prefers board games or surfing the internet?

Board games = 46%
Surfing internet = 9%
Since these are mutually exclusive (one person picks one favorite), we add them:

46 + 9 = 55%

As a probability: 55/100 = 11/20

b. Out of 500 people surveyed, how many would prefer books?

Books = 25% of 500

25% = 0.25 → 0.25 × 500 = 125 people

c. Is sample of 500 reasonable to expect same preferences?

Yes — larger samples tend to give more reliable results that reflect the population better. With 500 people, random variation is smaller, so we’d expect similar percentages as long as the group is representative.

Why? Because of the Law of Large Numbers — as sample size increases, experimental probability gets closer to theoretical (or true) probability.

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Problem 7: Spinner with Four Sections

Spinner sections: green, blue, yellow, red — spun 100 times.

Frequency table:

| Section | Frequency |
|---------|-----------|
| Green | 15 |
| Blue | 10 |
| Yellow | 7 |
| Red | 68 |

Check total: 15 + 10 + 7 + 68 = 100 → good.

a. Experimental probability of landing on green

Green frequency = 15
Total spins = 100

P(green) = 15/100 = 3/20

b. Expected probability of landing on red

This likely means *theoretical* probability — assuming spinner is fair.

There are 4 equal sections → each should have 1/4 chance.

So expected (theoretical) P(red) = 1/4

(Note: If they meant experimental, it would be 68/100 = 17/25, but wording says “expected”, which usually means theoretical.)

c. If spun 40 more times, how many times land on red?

Use experimental probability from first 100 spins: P(red) = 68/100 = 0.68

So in next 40 spins, expected number = 0.68 × 40 = ?

Calculate: 0.68 × 40 = (68/100) × 40 = (68 × 40)/100 = 2720 / 100 = 27.2

Since you can’t spin 0.2 times, round to nearest whole number → 27 times

(Because 27.2 is closer to 27 than 28? Actually, 0.2 is less than 0.5, so yes — 27)

But sometimes in probability, we leave as decimal or say “about 27”. Since question says “how many times”, probably expects integer.

Also note: This assumes the spinner behaves the same way — i.e., uses experimental probability from past data.

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Now compile final answers clearly.

Final Answer:

5a. 5/24
5b. 5/6
5c. Experimental P(not 6) = 19/24; Theoretical P(not 6) = 20/24 → very close, experimental slightly lower

6a. 11/20 (or 55%)
6b. 125 people
6c. Yes — larger samples reduce randomness and better reflect true preferences

7a. 3/20
7b. 1/4
7c. 27 times