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Worksheet: Experimental and Theoretical Probabilities

Q1:

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

Q2:

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

Q3:

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

Q4:

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

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 1 5
  • B 1 6
  • C 2 3
  • D 1 9 3 0

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 1 3
  • C0
  • D 2 3

Q8:

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

Q9:

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

Q10:

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

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

Q12:

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

Q13:

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

Q14:

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

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 224 839 287, what is the probability of the digit being even?

  • A 5 9
  • B 7 9
  • C 3 5
  • D 2 3

Q17:

The ratio of boys to girls at a school club is 4 ∢ 1 . If a student is chosen at random from the club, what is the probability that they are a girl?

  • A 1 6
  • B 4 5
  • C 2 5
  • D 1 5

Q18:

Given that the set { 1 , 5 , 8 } 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 3 5
  • B 1 3
  • C 7 9
  • D 2 3
  • E 8 9

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 3 3 5 0
  • B 3 1 5 0
  • C 1 7 5 0
  • D 1 9 5 0

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 7 1 2
  • B 4 9
  • C 1 9 3 6
  • D 5 9
  • E 1 1 1 8

Q21:

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

  • A 9 2 8
  • B 2 3
  • C 1 0 2 7
  • D 1 3
  • E 8 2 7

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 6 1 9 . Find the probability of choosing a red ball.

  • A 8 1 9
  • B 6 1 9
  • C 1 4 1 9
  • D 5 1 9

Q23:

There are 28 people in a meeting. The probability that a person chosen at random is a man is 1 2 . 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 5 6
  • C 1 3
  • D 1 6

Q25:

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