Math quiz on probability and statistics focusing on rolling a standard cube, with questions and multiple-choice answers.

Let’s solve each question step by step.

---

Question 1:

You roll a standard cube 10 times. Results:
6, 4, 6, 1, 5, 2, 4, 2, 4, 3

We are asked: What is P(rolling a 5)?

That means: out of the 10 rolls, how many times did we get a 5?

Look at the list:
Only one time — the fifth number is 5.

So, probability = (number of 5s) / (total rolls) = 1/10

✔ Answer: C → 1/10

---

Question 2:

Same results: 6, 4, 6, 1, 5, 2, 4, 2, 4, 3

What is P(rolling a 6)?

Count how many 6s: first and third → that’s two 6s.

Probability = 2/10 = 1/5

Wait — let’s check options:

A) 1/5
B) 3/10
C) 4/5
D) 1/10

2/10 simplifies to 1/5 → so A is correct.

But wait — double-check the list:
Positions:
1: 6
2: 4
3: 6 ← second 6
4: 1
5: 5
6: 2
7: 4
8: 2
9: 4
10: 3

Yes, only two 6s → 2/10 = 1/5

✔ Answer: A → 1/5

---

Question 3:

Same results: 6, 4, 6, 1, 5, 2, 4, 2, 4, 3

What is P(rolling an even number)?

Even numbers on a die: 2, 4, 6

Go through the list and count how many are even:

1. 6 → even ✔
2. 4 → even ✔
3. 6 → even ✔
4. 1 → odd ✘
5. 5 → odd ✘
6. 2 → even ✔
7. 4 → even ✔
8. 2 → even ✔
9. 4 → even ✔
10. 3 → odd ✘

Count the ✔: positions 1,2,3,6,7,8,9 → that’s 7 evens.

Total rolls: 10

Probability = 7/10

Options:

A) 7/10
B) 6/10
C) 1/10
D) 5/10

✔ Answer: A → 7/10

---

Question 4:

You are rolling a standard number cube (1 to 6). What is the probability of rolling a 5?

This is theoretical probability — not based on experimental data like before.

Standard cube has 6 faces: 1,2,3,4,5,6 → all equally likely.

Only one face shows 5.

So, P(rolling a 5) = 1/6

Options:

A) 2/3
B) 1/2
C) 1/6
D) 1/3

✔ Answer: C → 1/6

---

Question 5:

Same setup: standard cube (1 to 6). Probability of rolling a 6?

Again, theoretical.

One face out of six is 6 → so 1/6

Options:

A) 1/6
B) 2/3
C) 1/2
D) 1/3

✔ Answer: A → 1/6

---

Final Answer:

1. C
2. A
3. A
4. C
5. A