**Q4: **

A bag contains white, red, and black balls. The probability of drawing a white ball at random is and a red ball at random is . How many red balls and how many black balls are in the bag?

- A11, 3
- B11, 6
- C3, 6
- D6, 3
- E5, 4

**Q5: **

What is the expected number of tails when a fair coin is flipped 690 times?

- A357
- B339
- C327
- D346

**Q6: **

A bag contains an unknown number of balls. one-sixth of them are white, one-fifth of them are green, and the rest are blue. If a ball is drawn at random from the bag, what is the probability that it is blue?

- A
- B
- C
- D

**Q7: **

A bag contains 8 white balls and 4 red balls. If a ball is chosen at random from the bag, what is the probability that the ball is white?

- A1
- B
- C0
- D

**Q8: **

Suppose we roll a fair die twice and denote the sum of the results by . Calculate the probability that .

- A
- B
- C
- D

**Q9: **

Suppose is a sample space consisting of 14 equally like outcomes. Given and , find .

- A
- B
- C
- D

**Q10: **

Elizabeth wants to compare theoretical and experimental probabilities. She decides to roll a die 12 times, 120 times, and 1β200 times and then compare the three distributions.

After 12 rolls, she got the following results:

1 | 2 | 3 | 4 | 5 | 6 |

2 | 1 | 0 | 2 | 2 | 5 |

After 120 rolls, she got the following results:

1 | 2 | 3 | 4 | 5 | 6 |

23 | 18 | 35 | 13 | 15 | 16 |

After 1β200 rolls, she got the following results:

1 | 2 | 3 | 4 | 5 | 6 |

208 | 196 | 211 | 191 | 200 | 194 |

Elizabeth knows that the theoretical probability of rolling a 3 is , correct to three decimal places.

Using the experiment with 12 trials, calculate the experimental probability of rolling a 3.

Using the experiment with 120 trials, calculate the experimental probability of rolling a 3. Give your answer as a decimal to three decimal places.

Using the experiment with 1200 trials, calculate the experimental probability of rolling a 3. Give your answer as a decimal to three decimal places.

If Elizabeth were to continue rolling her dice and record 12β000 rolls, would you anticipate that the experimental probability for rolling a 3 would get closer to or further away from the theoretical probability?

- AFurther away from it
- BCloser to it

**Q11: **

A bag contains 28 balls, 10 of which are white, 9 are red, and 9 are black. If a ball is drawn at random, what is the probability of the ball being red?

- A
- B
- C
- D

**Q12: **

If a digit from the number 375β753β363 is selected at random, what is the probability that it is even?

- A0
- B
- C
- D

**Q13: **

Given that the set is used to write a two-digit number which may have repeated digits, determine the probability that the product of the digits of the number formed is 2.

- A
- B
- C
- D
- E

**Q14: **

Given that the set is used to write a two-digit number which has no repeated digits, determine the probability that the number formed is odd.

- A
- B
- C1
- D

**Q15: **

A bag contains 100 balls. There are 14 red balls, 49 blue balls, and the remaining balls are white. If a ball is taken from the bag at random, what is the probability that the ball is not white? Give your answer to three decimal places.

**Q16: **

If a single digit is selected at random from the number 224β839β287, what is the probability of the digit being even?

- A
- B
- C
- D

**Q17: **

The ratio of boys to girls at a school club is . If a student is chosen at random from the club, what is the probability that they are a girl?

- A
- B
- C
- D

**Q18: **

Given that the set is used to write a two-digit number which has no repeated digits, determine the probability that the tens digit is an odd number.

- A
- B
- C
- D
- E

**Q19: **

In a class of 50 students, 33 passed the mathematics test and 31 passed the language test. What is the probability that a randomly selected student failed the language test?

- A
- B
- C
- D

**Q20: **

A class of 36 students took a maths exam where the maximum mark was 50. If 16 students got less than 40 marks, what is the probability that a student got greater than or equal to 40 marks?

- A
- B
- C
- D
- E

**Q21: **

A class has 18 boys and 9 girls. What is the probability that a randomly selected student is a girl?

- A
- B
- C
- D
- E

**Q22: **

A bag contains 25 red balls, 30 blue balls, and an unknown number of yellow balls. Given that the probability of choosing a blue ball from the balls is . Find the probability of choosing a red ball.

- A
- B
- C
- D

**Q23: **

There are 28 people in a meeting. The probability that a person chosen at random is a man is . Calculate the number of women in the meeting.

**Q24: **

What is the probability of rolling a number divisible by 5 on a fair die?

- A0
- B
- C
- D

**Q25: **

What is the probability of rolling an even number greater than 1 on a fair die?

- A
- B
- C
- D