Worksheet: Experimental and Theoretical Probabilities

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

Q1:

For a single roll of a die, find the probability of getting an even number.

  • A 1 6
  • B 1 4
  • C 1 3
  • D 1 2
  • E 3 4

Q2:

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

  • A0
  • B 5 6
  • C 1 3
  • D 1 6

Q3:

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

  • A 2 3
  • B 1 6
  • C 1 3
  • D 1 2

Q4:

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

  • A 1 6
  • B 1 4
  • C1
  • D 1 2

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 7 1 1
  • B 9 1 1
  • C0
  • D1
  • E 2 1 1

Q7:

If a letter is randomly selected from the word β€œValencia” what is the probability that it is β€œE”?

  • A 1 4
  • B 0
  • C 1 7
  • D 1 8

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 5 1 3
  • B 9 1 3
  • C 3 1 3
  • D 4 1 3
  • E 1 0 1 3

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 2 3 8 4
  • B 5 7
  • C 2 5 8 4
  • D 2 7

Q10:

A bag contains 30 coloured marbles. The probability of choosing a white marble at random is 2 5 . How many white marbles are in the bag?

Q11:

The table shows the number of employees in each department of a company. If an employee is selected at random, what is the probability that they are part of the sales department?

Departments Marketing Finance Customer Service Warehouse IT Sales
Employees 5 8 25 6 4 2
  • A 1 2
  • B 4 2 5
  • C 3 2 5
  • D 1 2 5
  • E 2 2 5

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.

𝐻 (Hours of Use) 𝐻 < 1 5 0 1 5 0 ≀ 𝐻 < 4 0 0 4 0 0 ≀ 𝐻 < 1 0 0 0 1 0 0 0 β‰₯ 𝐻
Number of Lamps 150 320 270 260
  • A 2 7 1 0 0
  • B 1 7 2 0
  • C 4 7 1 0 0
  • D 3 2 0
  • E 8 2 5

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 1 2
  • B 1 5
  • C 7 1 0
  • D 3 1 0
  • E 2 5

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 1 1 0
  • B 2 5
  • C 1 5
  • D 3 1 0

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 1 5
  • B 1 6
  • C 1 2
  • D 1 4

What is Fares’s experimental probability for rolling a 2?

  • A 2 2 1 0 0
  • B 1 6
  • C 1 4
  • D 2 7 1 0 0

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 1 200 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 1 200 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 1 6 = 0 . 1 6 7 , 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 12 000 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 1 1 2 0 and a red ball at random is 3 1 0 . 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 1 5
  • B 1 6
  • C 2 3
  • D 1 9 3 0

Q19:

Suppose we roll a fair die twice and denote the sum of the results by 𝑆 . Calculate the probability that 5 < 𝑆 < 1 1 .

  • A 1 3 1 8
  • B 2 9 3 6
  • C 1 1 1 2
  • D 2 3 3 6

Q20:

Suppose 𝑆 is a sample space consisting of 14 equally like outcomes. Given 𝐴 βŠ‚ 𝑆 and 𝑛 ( 𝐴 ) = 1 3 , find 𝑃 ( 𝐴 ) .

  • A 6 7
  • B 1 1 4
  • C 1 1 1 4
  • D 1 3 1 4

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 1 9 2 8
  • B 5 1 4
  • C 9 1 9
  • D 9 2 8

Q22:

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

  • A0
  • B 2 9
  • C 1 1 0
  • D 1 9

Q23:

Given that the set { 2 , 1 } 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 1 4
  • B 1 3
  • C 2 3
  • D 1 2
  • E 3 4

Q24:

Given that the set { 4 , 7 } is used to write a two-digit number which has no repeated digits, determine the probability that the number formed is odd.

  • A 3 4
  • B 2 5
  • C1
  • D 1 2

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.

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