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Probability basics · 2 marks

Fill in the blanks.

  1. (i) The probability of an impossible event is _______.
  2. (ii) The set of all possible outcomes of a random experiment is called the __________.
  3. (iii) The probability of an event that is certain to happen is _______.
  4. (iv) Tossing a fair coin has a probability of ______ for getting heads.
Answer: (i) 0 (ii) sample space (iii) 1 (iv) 12 (0.5)

Step-by-step solution

Idea: Probability runs from 0 (impossible) to 1 (certain). The list of all possible outcomes is the sample space. A fair coin has 2 equally likely outcomes.

(i) The probability of an impossible event is _______.

  1. An impossible event can never happen; it sits at the bottom of the probability scale: 0.½ mark
0

(ii) The set of all possible outcomes of a random experiment is called the __________.

  1. The list of all possible outcomes, written S, is the sample space.½ mark
sample space

(iii) The probability of an event that is certain to happen is _______.

  1. A certain event always happens; it sits at the top of the probability scale: 1.½ mark
1

(iv) Tossing a fair coin has a probability of ______ for getting heads.

  1. S = {H, T}: 2 equally likely outcomes, 1 favourable. P(heads) = 12 = 0.5.½ mark
12
(i) 0 (ii) sample space (iii) 1 (iv) 1/2

Check: Every probability lies between the answers to (i) and (iii): 0 ≤ P(E) ≤ 1. The answer to (iv), 0.5, is in the middle: an even chance.

Answer to write in the exam

(i)

∴ The probability of an impossible event is 0.

(ii)

∴ The set of all possible outcomes of a random experiment is called the sample space.

(iii)

∴ The probability of an event that is certain to happen is 1.

(iv)

S = {H, T}; P(H) = 12

∴ Tossing a fair coin has a probability of 12 for getting heads.

Common mistakes that cost marks

  • Writing “−1” or “none” for an impossible event. Probability is never negative; impossible means 0.
  • Writing “100” for a certain event. As a percentage it is 100%, but as a probability it is 1.
  • Writing “event” or “outcome” in (ii). One outcome is a single result; the set of all of them is the sample space.

How this can come in the exam

MCQ (1 mark)

Which of the following cannot be the probability of an event?

  1. 0
  2. 0.75
  3. 32
  4. 1
Show answer

(C) 32
32 = 1.5 is greater than 1, and every probability lies between 0 and 1.

Assertion–Reason (1 mark)

Assertion (A): When an ordinary die is thrown once, the sample space is {2, 4, 6}.
Reason (R): The sample space is the set of all possible outcomes of a random experiment.

  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Show answer

(D) A is false but R is true.
{2, 4, 6} lists only the even outcomes, so it is an event, not the sample space. The sample space is {1, 2, 3, 4, 5, 6}, so A is false. R is the correct meaning of sample space, so R is true.

Try one yourself

Fill in the blank: an event that is as likely to happen as not has probability ______.

Show answer

12 (0.5): an even chance.

More questions like this

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