Worksheet: Experimental Probability

In this worksheet, we will practice interpreting a data set by finding and evaluating the experimental probability.

Q1:

Two coins are tossed 76 times. The upper faces are observed, and the results are recorded in this table. Determine the experimental probability of getting two tails as a fraction in its simplest form.

Tails 0 1 2
Number of Occurrences 32 28 16
  • A 1 2
  • B 4 1 9
  • C 7 1 9
  • D1
  • E 8 1 9

Q2:

The table shows the results of a survey that asked 20 students about their favorite breakfast.

Breakfast Eggs Cereal Toast
Number of Students 10 2 8

What is the probability that a randomly selected student prefers eggs?

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

Q3:

A biased coin was tossed 350 times and the number of tails observed was 178. Calculate the relative frequency of getting heads.

  • A172
  • B 8 9 1 7 5
  • C 8 6 1 7 5
  • D 1 2

Q4:

A six-sided die contains the numbers 1 to 6. It was rolled 26 times and the number of times each value appeared is shown in the table. Find the experimental probability of rolling a 4.

Value 1 2 3 4 5 6
Frequency 8 4 4 2 5 3
  • A 2 1 3
  • B 5 2 6
  • C 1 1 3
  • D 1 6

Q5:

A soft drinks factory produces 1,400 bottles a day. The factory tested a sample of 400 units and found that 6 were defective. By calculating the experimental probability that a bottle is defective, work out how many defective bottles would be expected in a day.

Q6:

A boy flipped a coin 100 times, and he got heads 58 times. Calculate his experimental probability of getting heads while playing this game.

Q7:

The given fair spinner was spun 248 times. What is the expected number of times the pointer will land on the section labeled by the letter 𝐹?

Q8:

A fair spinner has 8 equal sections, one of which is green. If the spinner is spun 56 times, what is the expected number of times it will stop on the green section?

Q9:

A fair die is rolled 136 times. Calculate the expected number of times a number greater than 3 is rolled.

Q10:

A fair die is rolled 150 times. What is the expected number of times for an odd number greater than 2 to be rolled?

Q11:

A fair die is rolled 150 times. What is the expected number of times for a number divisible by 3 to be rolled?

Q12:

A bag contains 9 blue, 5 red, 3 white, and 8 green marbles. If a marble is drawn at random and replaced 75 times, determine the expected number of times a green marble could be drawn.

Q13:

A game at a festival challenged people to throw a baseball through a tire. Of the first 68 participants, 3 people won the gold prize, 12 won the silver prize, and 15 won the bronze prize. What is the experimental probability of not winning any of the three prizes?

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

Q14:

On an irregular die, the probability of rolling the number 1, 2, 3, 4, or 5 is equal. The probability of rolling a 6 is three times that of any other number. What is the probability of rolling the number 5?

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

Q15:

A die is rolled 750 times. What is the expected number of times for an even number that is greater than 1 to be rolled?

Q16:

What is the probability of getting heads when a fair coin is flipped?

  • A 1 4
  • B 1 2
  • C1
  • D0

Q17:

What is the probability of getting heads when a fair coin is flipped?

  • A 3 4
  • B1
  • C 1 2
  • D 1 3

Q18:

What is the probability of getting tails when a fair coin is flipped?

  • A 1 4
  • B0
  • C 1 2
  • D1

Q19:

If a coin is flipped once, what is the probability of getting a head?

  • A 1 4
  • B1
  • C0
  • D 1 2

Q20:

Which of the following sets represents the event of rolling two numbers which sum to 10 on two six-sided dice?

  • A { ( 4 , 6 ) , ( 6 , 4 ) , ( 5 , 5 ) }
  • B { ( 5 , 6 ) , ( 6 , 4 ) , ( 5 , 5 ) }
  • C { ( 4 , 4 ) , ( 6 , 6 ) , ( 5 , 5 ) }
  • D { ( 4 , 6 ) , ( 6 , 4 ) , ( 6 , 5 ) }
  • E { ( 4 , 6 ) , ( 6 , 5 ) , ( 5 , 5 ) }

Q21:

If a fair number cube, labeled with the numbers 1–6, is rolled 90 times, which result is most likely to occur?

  • AThe number cube will land on a number larger than 4 about 15 times.
  • BThe number cube will land on 6 about 30 times.
  • CThe number cube will land on a prime number about 60 times.
  • DThe number cube will land on an odd number about 45 times.

Q22:

Suppose you roll two number cubes, where each cube has the numbers 1, 2, 3, 4, 5, and 6 on its faces. Determine the probability that the sum of the two numbers rolled is less than 12.

  • A 1 3 6
  • B 1 1 8
  • C1
  • D 3 5 3 6
  • E0

Q23:

Two fair dice are rolled. Which of the following represents the event of rolling two numbers which sum to 7?

  • A 𝐴 = { ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1 ) }
  • B 𝐴 = { ( 1 , 6 ) , ( 2 , 5 ) , ( 3 , 4 ) }
  • C 𝐴 = { ( 1 , 6 ) , ( 2 , 5 ) , ( 3 , 4 ) , ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1 ) }
  • D 𝐴 = { ( 1 , 6 ) , ( 2 , 5 4 ) , ( 3 , 3 ) , ( 3 , 4 ) , ( 5 , 2 ) , ( 6 , 1 ) }

Q24:

A die is rolled two consecutive times. Which of the following represents the event of rolling two numbers which have a difference of 2?

  • A 𝐴 = { ( 1 , 4 ) , ( 4 , 1 ) , ( 2 , 5 ) , ( 5 , 2 ) , ( 3 , 6 ) , ( 6 , 3 ) }
  • B 𝐴 = { ( 1 , 3 ) , ( 2 , 4 ) , ( 3 , 5 ) , ( 4 , 6 ) }
  • C 𝐴 = { ( 1 , 3 ) , ( 3 , 1 ) , ( 2 , 4 ) , ( 4 , 2 ) , ( 3 , 5 ) , ( 5 , 3 ) , ( 4 , 6 ) , ( 6 , 4 ) }
  • D 𝐴 = { ( 3 , 1 ) , ( 4 , 2 ) , ( 5 , 3 ) , ( 6 , 4 ) }

Q25:

A fair die is rolled twice. What is the probability of rolling two numbers which sum to an even number less than 4?

  • A 7 1 8
  • B 1 3 6
  • C0
  • D 1 1 2

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