Events in Probability Practice Questions

Last Updated : 1 Oct, 2026

An event in probability is a specific outcome or a group of outcomes of a random experiment. Since every event consists of outcomes from the sample space, an event is always a subset of the sample space.

Example: When a die is rolled, the sample space is S = {1, 2, 3, 4, 5, 6}.
The event "getting an even number" is E = {2, 4, 6}, which is a subset of the sample space.

Solved Examples

Question 1: Consider the experiment of tossing a fair coin 3 times. Event A is defined as getting all tails. What kind of event is this. 

Solution: 

Sample space for the coin toss will be, 

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

For the event A, 
A = {TTT}

This event is only mapped to one element of sample space. Thus, it is a simple event. 

Question 2: The sample Space of an experiment is given as,

S = {10, 11, 12, 13, 14, 15, 16, 17} and the event, E is defined as all the even numbers. What will be the complementary event for E.

Solution:

S = {10, 11, 12, 13, 14, 15, 16, 17}
E (All even numbers) = {10, 12, 14, 16}
E' (complementary of E) = {11, 13, 15, 17}

Question 3: A die is thrown in the game of Ludo, and E1 denotes the event of getting even numbers and E2 represents the event of getting a number more than 3. Find the Set for the following events,

  1. E1 or E2
  2. E1 and E2

Solution:

The sample space for the die will be,
S = {1, 2, 3, 4, 5, 6}

  • E1 (only even numbers) = {2, 4, 6}
  • E2 (number more than 3) = {4, 5, 6}
  1. E1 or E2 = {2, 4, 5, 6}
  2. E1 and E2 = {4, 6}

Question 4: A die is rolled, and three events A, B, and C are defined below:

  • A: Getting a number greater than 3 
  • B: Getting a number that is a multiple of 3. 
  • C: Getting an odd number

Find A ∩ B, A ∩ B ∩ C, and A ∪ B.

Solution:

Sample space for die roll will be, 
S = {1, 2, 3, 4, 5, 6} 

For the event A, 
A = {4, 5, 6}

For the event B, 

B = {3, 6}

For the event C, 
C = {1, 3, 5}

A ∩ B = {4, 5, 6} ∩ {3, 6}
A ∩ B = {6}

A ∩ B ∩ C = {4, 5, 6} ∩ {3, 6} ∩ {1, 3, 5}
A ∩ B ∩ C = ∅ (Empty Set) 

A ∪ B = {4, 5, 6} ∪ {3, 6}
A ∪ B = {3, 4, 5, 6}

Practice Questions

Question 1: Two coins are tossed simultaneously. Let: A = event of getting at least one head, B = event of getting both tails.

Find:

  1. Sample space S
  2. Events A and B
  3. Are A and B mutually exclusive?

Question 2: A die is thrown twice. Let E be the event that the sum of the numbers obtained is greater than 8, and F be the event that both numbers are even. List all outcomes in E, F, and E ∩ F.

Question 3: Three coins are tossed together. Let: A = event of getting exactly two heads, B = event of getting at least one tail.

Find the sets A, B, and A ∩ B, and state whether A and B are independent.

Determine whether E1 and E2 are independent events.

Question 4: A die is rolled once. Let: A = event of getting an odd number, B = event of getting a number greater than 3, C = event of getting a prime number.

Find:

  1. A ∩ B
  2. A ∩ C
  3. A ∩ B ∩ C
  4. Are A, B, and C mutually exclusive?
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