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Worksheet: Sample Space and Probability

Q1:

A card is drawn at random from a pack of cards numbered from 1 to 32. Write the set of outcomes that the number on the card is odd and divisible by 3?

  • A { 1 , 3 , 5 , 7 , 9 , 1 1 , 1 3 , 1 5 , 1 7 , 1 9 , 2 1 , 2 3 , 2 5 , 2 7 , 2 9 , 3 1 }
  • B { 6 , 1 2 , 1 8 , 2 4 , 3 0 }
  • C { 2 , 4 , 6 , 8 , 1 0 , 1 2 , 1 4 , 1 6 , 1 8 , 2 0 , 2 2 , 2 4 , 2 6 , 2 8 , 3 0 , 3 2 }
  • D { 3 , 9 , 1 5 , 2 1 , 2 7 }
  • E { 3 , 6 , 9 , 1 2 , 1 5 , 1 8 , 2 1 , 2 4 , 2 7 , 3 0 }

Q2:

Which of the following represents the sample space of choosing at random a prime number between 3 and 59?

  • A 𝑆 = { 7 , 1 1 , 1 3 , 1 7 , 1 9 , 2 3 , 2 9 , 3 1 , 3 7 , 4 1 , 4 3 , 4 7 }
  • B 𝑆 = { 2 , 3 , 5 , 7 , 1 1 , 1 3 , 1 7 , 1 9 , 2 3 , 2 9 , 3 1 , 3 7 , 4 1 , 4 3 , 4 7 , 5 3 , 5 9 }
  • C 𝑆 = { 5 , 7 , 1 1 , 1 3 , 1 7 , 1 9 , 2 3 , 2 9 , 3 1 , 3 7 , 4 1 , 4 3 }
  • D 𝑆 = { 5 , 7 , 1 1 , 1 3 , 1 7 , 1 9 , 2 3 , 2 9 , 3 1 , 3 7 , 4 1 , 4 3 , 4 7 , 5 3 }
  • E 𝑆 = { 7 , 1 1 , 1 3 , 1 7 , 1 9 , 2 3 , 2 9 , 3 1 , 3 7 , 4 1 , 4 3 }

Q3:

Two distinct digits are chosen at random from the set { 1 , 2 , 4 , 8 } . What is the probability that either of the digits is an odd number?

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

Q4:

I write a two-digit number by randomly picking each digit from the set { 2 , 3 , 4 , 5 , 7 , 8 } , where a digit can be repeated. Write the set of outcomes that is the event that the number is prime.

  • A { 2 3 , 2 5 , 2 7 , 3 3 , 3 5 , 3 7 , 4 3 , 4 5 , 4 7 , 5 3 , 5 5 , 5 7 , 7 3 , 7 5 , 7 7 , 8 3 , 8 5 , 8 7 }
  • B { 2 4 , 2 7 , 3 3 , 4 2 , 4 5 , 4 8 , 5 4 , 5 7 , 7 2 , 7 5 , 7 8 , 8 4 , 8 7 }
  • C { 2 2 , 2 4 , 2 8 , 3 2 , 3 4 , 3 8 , 4 2 , 4 4 , 4 8 , 5 2 , 5 4 , 5 8 , 7 2 , 7 4 , 7 8 , 8 2 , 8 4 , 8 8 }
  • D { 2 3 , 3 7 , 4 3 , 4 7 , 5 3 , 7 3 , 8 3 }
  • E { 2 5 , 3 5 , 4 5 , 5 5 , 7 5 , 8 5 }

Q5:

In an experiment a coin is flipped repeatedly until the first time it lands heads side up, or until it lands tails side up three times in a row. Determine the set for event 𝐴 , which is the appearance of at least two tails.

  • A 𝐴 = { ( , ) , ( , , ) } T H T T T
  • B 𝐴 = { ( , , ) } T T T
  • C 𝐴 = { ( , ) , ( , , ) , ( , , ) } T H T T H T T T
  • D 𝐴 = { ( , , ) , ( , , ) } T T H T T T
  • E 𝐴 = { ( , , ) , ( , , ) } H H T H H H

Q6:

A bag contains 4 red balls and 6 brown balls. Which of the following represents the sample space of choosing a ball at random and recording its color?

  • A{brown}
  • B{red}
  • C{red, red}
  • D{red, brown}
  • E{brown, brown}

Q7:

In an experiment a coin is repeatedly flipped until it lands head side up, or it lands tail side up three times in a row. Determine the set representing event 𝐴 , which is the appearance of at least one head.

  • A 𝐴 = { , ( , ) , ( , , ) , ( , , ) } H T H T T H T T T
  • B 𝐴 = βˆ…
  • C 𝐴 = { ( , ) , ( , , ) , ( , , ) } T H T T H T T T
  • D 𝐴 = { , ( , ) , ( , , ) } H T H T T H
  • E 𝐴 = { , ( , ) , ( , , ) , ( , , , , ) } H T H T T H T T T H H

Q8:

Given that the sample space is the set of all 2-digit numbers whose digits are different and belong to , write the event that the number is odd.

  • A
  • B
  • C
  • D
  • E

Q9:

What is the probability of choosing at random, two numbers which sum to 9, from the set { 1 , 5 , 7 , 8 } ? You are allowed to pick the same number more than once.

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

Q10:

In a random experiment, a ball is chosen at random from a box that contains four balls: one blue, one purple, one brown, and one white. List all the possible outcomes of this experiment.

  • A{blue, white, gray, purple}
  • B{blue, purple, brown}
  • C{brown, white, purple}
  • D{purple, blue, brown, white}
  • E{purple, white, brown, orange}

Q11:

I write a two-digit number by randomly picking each digit from the set { 2 , 4 , 8 } , where a digit can be repeated. What is the probability that the product of the two digits is 32?

  • A 3 1 0
  • B 1 3
  • C 1 5
  • D 2 9
  • E 4 9

Q12:

In an experiment a coin is repeatedly flipped until it lands head side up or it lands tail side up three times in a row. Determine the subset of the experiment's sample space representing event 𝐴 , which is the appearance of at least two heads.

  • A 𝐴 = { ( , ) , ( , , ) } T H T T T
  • B 𝐴 = { ( , , ) , ( , , ) } T T H T T T
  • C 𝐴 = { , ( , ) , ( , , ) , ( , , ) } H T H T T H T T T
  • D 𝐴 = βˆ…
  • E 𝐴 = { ( , , ) , ( , , ) } T H H H H H

Q13:

A bag contains 20 identical cards numbered 1 to 20. A card is selected at random, and the number written on it is recorded. Write the set representing event 𝐴 , where the recorded number, π‘₯ , satisfies the inequality 5 π‘₯ βˆ’ 3 ≀ 1 7 .

  • A 𝐴 = { 4 , 5 , 6 , 7 , 8 , 9 , 1 0 , 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 , 1 9 , 2 0 }
  • B 𝐴 = { 1 , 2 , 3 }
  • C 𝐴 = { 4 }
  • D 𝐴 = { 1 , 2 , 3 , 4 }
  • E 𝐴 = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 1 0 , 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 , 1 9 , 2 0 }

Q14:

Two separate regular dice are rolled, and the numbers on their upper faces noted. Write down the sample space of the event 𝐴 , which is the appearance of two numbers such that one of them is twice the other.

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

Q15:

I write a two-digit number by randomly selecting two different digits from the set { 1 , 2 , 3 , 4 , 5 , 6 , 8 } . Which of the following represents the event that there is an odd digit in the tens position?

  • A { 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 8 , 3 1 , 3 2 , 3 3 , 3 4 , 3 5 , 3 6 , 3 8 , 5 1 , 5 2 , 5 3 , 5 4 , 5 5 , 5 6 , 5 8 }
  • B { 1 3 , 1 5 , 2 1 , 2 3 , 2 5 , 3 1 , 3 5 , 4 1 , 4 3 , 4 5 , 5 1 , 5 3 , 6 1 , 6 3 , 6 5 , 8 1 , 8 3 , 8 5 }
  • C { 2 1 , 2 2 , 2 3 , 2 4 , 2 5 , 2 6 , 2 8 , 4 1 , 4 2 , 4 3 , 4 4 , 4 5 , 4 6 , 4 8 , 6 1 , 6 2 , 6 3 , 6 4 , 6 5 , 6 6 , 6 8 , 8 1 , 8 2 , 8 3 , 8 4 , 8 5 , 8 6 , 8 8 }
  • D { 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 8 , 3 1 , 3 2 , 3 4 , 3 5 , 3 6 , 3 8 , 5 1 , 5 2 , 5 3 , 5 4 , 5 6 , 5 8 }
  • E { 1 1 , 1 3 , 1 5 , 2 1 , 2 3 , 2 5 , 3 1 , 3 3 , 3 5 , 4 1 , 4 3 , 4 5 , 5 1 , 5 3 , 5 5 , 6 1 , 6 3 , 6 5 , 8 1 , 8 3 , 8 5 }

Q16:

Write, as a subset of the sample space, the event of rolling a number greater than 1 on a fair die.

  • A { 2 , 4 , 6 }
  • B { 1 , 3 , 5 }
  • C { 3 , 6 }
  • D { 2 , 3 , 4 , 5 , 6 }
  • E { 1 , 2 , 3 , 4 , 5 , 6 }

Q17:

A fair coin is flipped and and a fair dice is rolled. Which of the following represents the event of rolling a number which is divisible by 3?

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

Q18:

I write a two-digit number by randomly picking each digit from the set { 2 , 3 , 4 , 5 , 7 , 8 , 9 } , where digits can be repeated. Which of the following is the event that the number is odd?

  • A { 2 2 , 2 4 , 2 8 , 3 2 , 3 4 , 3 8 , 4 2 , 4 4 , 4 8 , 5 2 , 5 4 , 5 8 , 7 2 , 7 4 , 7 8 , 8 2 , 8 4 , 8 8 , 9 2 , 9 4 , 9 8 }
  • B { 3 2 , 3 3 , 3 4 , 3 5 , 3 7 , 3 8 , 3 9 , 5 2 , 5 3 , 5 4 , 5 5 , 5 7 , 5 8 , 5 9 , 7 2 , 7 3 , 7 4 , 7 5 , 7 7 , 7 8 , 7 9 , 9 2 , 9 3 , 9 4 , 9 5 , 9 7 , 9 8 , 9 9 }
  • C { 2 4 , 2 8 , 3 2 , 3 4 , 3 8 , 4 2 , 4 8 , 5 2 , 5 4 , 5 8 , 7 2 , 7 4 , 7 8 , 8 2 , 8 4 , 9 2 , 9 4 , 9 8 }
  • D { 2 3 , 2 5 , 2 7 , 2 9 , 3 3 , 3 5 , 3 7 , 3 9 , 4 3 , 4 5 , 4 7 , 4 9 , 5 3 , 5 5 , 5 7 , 5 9 , 7 3 , 7 5 , 7 7 , 7 9 , 8 3 , 8 5 , 8 7 , 8 9 , 9 3 , 9 5 , 9 7 , 9 9 }
  • E { 2 3 , 2 5 , 2 7 , 2 9 , 3 5 , 3 7 , 3 9 , 4 3 , 4 5 , 4 7 , 4 9 , 5 3 , 5 7 , 5 9 , 7 3 , 7 5 , 7 9 , 8 3 , 8 5 , 8 7 , 8 9 , 9 3 , 9 5 , 9 7 }

Q19:

Which of the following denotes the sample space of selecting an even number between 39 and 52 at random?

  • A 𝑆 = { 3 8 , 4 0 , 4 2 , 4 4 , 4 6 , 4 8 , 5 0 , 5 2 }
  • B 𝑆 = { 4 0 , 4 2 , 4 4 , 4 6 , 4 8 , 5 0 , 5 2 }
  • C 𝑆 = { 4 0 , 4 4 , 4 8 }
  • D 𝑆 = { 4 0 , 4 2 , 4 4 , 4 6 , 4 8 , 5 0 }
  • E 𝑆 = { 4 2 , 4 4 , 4 6 , 4 8 , 5 0 }

Q20:

Which of the following denotes the sample space of selecting an even number between 37 and 54 at random?

  • A 𝑆 = { 3 6 , 3 8 , 4 0 , 4 2 , 4 4 , 4 6 , 4 8 , 5 0 , 5 2 , 5 4 }
  • B 𝑆 = { 3 8 , 4 0 , 4 2 , 4 4 , 4 6 , 4 8 , 5 0 , 5 2 , 5 4 }
  • C 𝑆 = { 4 0 , 4 4 , 4 8 , 5 2 }
  • D 𝑆 = { 3 8 , 4 0 , 4 2 , 4 4 , 4 6 , 4 8 , 5 0 , 5 2 }
  • E 𝑆 = { 4 0 , 4 2 , 4 4 , 4 6 , 4 8 , 5 0 , 5 2 }

Q21:

Which of the following is the definition of a sample space?

  • A the set of some possible outcomes of a random experiment
  • B one of the possible outcomes of a random experiment
  • C the set of all the possible outcomes of a random experiment

Q22:

A fair coin is flipped and a fair die is rolled. Which of the following represents the event of the coin landing tail-side up and an even number on the die?

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

Q23:

Two fair dice are rolled. Which of the following represents the event of rolling the same number on both dice?

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

Q24:

Which of the following represents the sample space of flipping a coin and rolling a die?

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

Q25:

I write a two-digit number by randomly picking each digit from the set { 2 , 4 , 5 , 6 } , where digits can be repeated. Write the set that represents the event that the number is divisible by 7.

  • A { 2 4 , 4 4 , 5 2 , 5 6 , 6 4 }
  • B { 2 4 , 4 2 , 4 5 , 5 4 , 6 6 }
  • C { 2 5 , 4 5 , 5 5 , 6 5 }
  • D { 4 2 , 5 6 }
  • E { 2 4 , 4 2 , 5 4 , 6 6 }