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Worksheet: Constructing Sample Space Using Tree Diagrams or Lists

Q1:

I write a two-digit number by randomly picking each digit to be either 3 or 7, where digits can be repeated. Write the set of all possible outcomes.

  • A { 3 3 , 7 7 }
  • B { 3 7 , 7 3 }
  • C { 3 7 3 , 7 3 7 , 3 3 7 , 7 7 3 }
  • D { 3 7 , 3 3 , 7 3 , 7 7 }
  • E { 3 7 3 , 7 3 7 }

Q2:

A bag contains 7 balls which are numbered 1 to 7. Determine the sample space of choosing a ball at random.

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

Q3:

Which of the following describes the sample space of a random experiment?

  • AThe set of all impossible outcomes of a random experiment.
  • BThe set of some possible outcomes of a random experiment.
  • CAn experiment which we can determine all its possible outcomes.
  • DThe set of all possible outcomes of a random experiment.

Q4:

A coin is flipped three times. Which of the following is the event that at least two tails appear?

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

Q5:

Which of the following represents the sample space of choosing a digit at random from the number 148 250?

  • A 𝑆 = { 1 , 2 , 4 , 5 }
  • B 𝑆 = { 0 , 1 , 2 , 4 , 5 }
  • C 𝑆 = { 2 , 4 , 5 }
  • D 𝑆 = { 0 , 1 , 2 , 4 , 5 , 8 }

Q6:

A bag contains 10 balls numbered from 32 to 41. Which of the following is the sample space for the experiment of choosing a numbered ball at random?

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

Q7:

Upon rolling a die and flipping a coin once, is the event of getting tails and an even number, is the event of getting heads and an odd number, and is the event of the nonoccurence of or the nonoccurence of . Determine the outcomes in the event .

  • A
  • B
  • C
  • D