In this worksheet, we will practice finding and comparing between experimental and theoretical probabilities.

**Q2: **

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

- A0
- B
- C
- D

**Q3: **

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

- A
- B
- C
- D

**Q4: **

Upon rolling a die once, determine the probability of getting a prime number.

- A
- B
- C1
- D

**Q5: **

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

- A357
- B339
- C327
- D346

**Q6: **

A bag contains 9 white balls and 2 red balls. If a ball is chosen at random from the bag, what is the probability that the ball is white or red?

- A
- B
- C0
- D1
- E

**Q8: **

A shop weighed a sample of 13 packets of chips that were supposed to weigh 25 g each. They found that 4 packets weighed less than 25 g, and the rest of the packets weighed more than 25 g. What is the probability that a packet of chips weighed less than it was supposed to?

- A
- B
- C
- D
- E

**Q9: **

A box contains two colours of balls: red and white. There are 60 red balls in the box and 84 balls in total. What is the probability of selecting a white ball at random?

- A
- B
- C
- D

**Q10: **

A bag contains 30 coloured marbles. The probability of choosing a white marble at random is . How many white marbles are in the bag?

**Q12: **

A light bulb manufacturer examined a sample of 1000 light bulbs from its production. Using the table which shows the results for this sample, calculate the experiment probability that a light bulb fails after less than 150 hours of use.

(Hours of Use) | ||||
---|---|---|---|---|

Number of Lamps | 150 | 320 | 270 | 260 |

- A
- B
- C
- D
- E

**Q13: **

A survey of 10 students found that 5 students preferred art, 2 preferred history, and 3 preferred science. What is the probability that a student preferred science?

- A
- B
- C
- D
- E

**Q14: **

The table shows the results of a survey that asked 30 students to vote for their favourite sport.

Sport | Football | Basketball | Volleyball | Swimming |
---|---|---|---|---|

Number of Students | 12 | 9 | 3 | 6 |

What is the probability that a randomly selected student voted for basketball?

- A
- B
- C
- D

**Q15: **

Fares has bought a tetrahedral die that has the values 1 to 4 on its faces. He wants to investigate whether the die is fair, so he decides to roll it 100 times and record all the values in a table. He gets the following results.

1 | 2 | 3 | 4 |

23 | 27 | 22 | 28 |

What is the theoretical probability of rolling a 2, assuming that the die is fair?

- A
- B
- C
- D

What is Faresβs experimental probability for rolling a 2?

- A
- B
- C
- D

Does the difference in these two probabilities mean that the die is most likely to be biased or unbiased?

- ABiased
- BUnbiased

**Q16: **

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

**Q17: **

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

**Q18: **

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

**Q19: **

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

- A
- B
- C
- D

**Q20: **

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

- A
- B
- C
- D

**Q21: **

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

**Q22: **

If a digit from the number 375,753,363 is selected at random, what is the probability that it is even?

- A0
- B
- C
- D

**Q23: **

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

**Q24: **

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

**Q25: **

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.