📌 1. What is Probability?
Probability is the branch of mathematics that measures chance or likelihood of an event.
👉 It tells how likely something is to happen.
📌 2. Formula of Probability
Probability (P)=Total number of outcomesNumber of favourable outcomes
📌 3. Types of Events
🔹 Certain Event
- Event that will definitely happen
- Probability = 1
🔹 Impossible Event
- Event that cannot happen
- Probability = 0
🔹 Simple Event
- One outcome only
🔹 Equally Likely Events
- All outcomes have same chance
📌 4. Sample Space
Set of all possible outcomes of an experiment.
👉 Example: Tossing a coin
Sample space = {H, T}
📌 5. Events
An event is a subset of sample space.
📌 6. Probability Values
- Always between 0 and 1
- 0 → impossible
- 1 → certain
📌 7. Examples
Coin Toss
- Head or Tail → each probability = 1/2
Dice Roll
- Total outcomes = 6
- Probability of getting 3 = 1/6
📌 8. Real-Life Use
- Weather forecasting
- Games (dice/cards)
- Risk prediction
- Decision making
TEST
📘 Probability: Basics, Sample Space & Events
🔹 SECTION A: MCQs (1–70)
1. Probability measures:
A) size B) chance C) length D) weight
Ans: B
2. Probability value lies between:
A) 1 and 10 B) 0 and 100 C) 0 and 1 D) -1 and 1
Ans: C
3. Formula of probability is:
A) total/favourable
B) favourable/total
C) total + favourable
D) total − favourable
Ans: B
4. Certain event probability is:
A) 0 B) 1 C) 1/2 D) 2
Ans: B
5. Impossible event probability is:
A) 0 B) 1 C) 1/2 D) 10
Ans: A
6. Sample space means:
A) possible outcomes B) impossible outcomes C) events D) numbers
Ans: A
7. Tossing a coin sample space is:
A) {1,2} B) {H,T} C) {0,1} D) {HH}
Ans: B
8. Rolling a dice sample space has:
A) 4 outcomes B) 5 outcomes C) 6 outcomes D) 8 outcomes
Ans: C
9. Probability of getting head in coin toss:
A) 1 B) 1/2 C) 0 D) 2
Ans: B
10. Probability of getting 3 on dice:
A) 1/6 B) 1/3 C) 1/2 D) 1
Ans: A
11. Equally likely events mean:
A) different chances B) same chances C) no chance D) impossible
Ans: B
12. Event is:
A) full set B) subset of sample space C) number D) graph
Ans: B
13. Probability of sure event is:
A) 0 B) 1 C) 1/2 D) undefined
Ans: B
14. Probability of impossible event is:
A) 0 B) 1 C) 2 D) -1
Ans: A
15. If probability = 0.5 then event is:
A) impossible B) certain C) equally likely D) random
Ans: C
16. Total outcomes of dice:
A) 4 B) 5 C) 6 D) 7
Ans: C
17. Probability of even number on dice:
A) 1/2 B) 1/3 C) 2/3 D) 1
Ans: A
18. Even numbers on dice are:
A) 1,3,5 B) 2,4,6 C) 1,2,3 D) 4,5,6
Ans: B
19. Probability of getting 7 on dice:
A) 0 B) 1/6 C) 1 D) 2
Ans: A
20. Head or Tail are:
A) events B) sample space C) outcomes D) numbers
Ans: C
📝 SECTION B: ASSERTION–REASON (71–85)
A: Both true, R explains A
B: Both true, R not explanation
C: A true, R false
D: A false, R true
71. A: Probability is always between 0 and 1
R: It measures chance of event
Ans: A
72. A: Impossible event has probability 1
R: It always happens
Ans: D
73. A: Sample space of coin is {H,T}
R: Coin has two outcomes
Ans: A
74. A: Dice has 8 outcomes
R: It has numbers 1 to 6
Ans: C
75. A: Certain event probability is 1
R: It will definitely happen
Ans: A
📊 SECTION C: NUMERICALS (86–95)
86. Probability of head in coin toss =
👉 1/2
87. Probability of 2 on dice =
👉 1/6
88. Probability of even number =
👉 3/6 = 1/2
89. Probability of odd number =
👉 3/6 = 1/2
90. Probability of number > 4 =
👉 2/6 = 1/3
91. Total outcomes of two coins =
👉 4
92. Sample space of two coins =
👉 {HH, HT, TH, TT}
93. Probability of getting TT =
👉 1/4
94. Probability of not getting head =
👉 1/2
95. Probability of getting number 1–6 =
👉 1
📄 SECTION D: VERY SHORT ANSWERS (96–100)
96. Define probability
👉 Measure of chance of event
97. What is sample space?
👉 All possible outcomes
98. What is event?
👉 Subset of sample space
99. Range of probability?
👉 0 to 1
100. Probability of impossible event?
👉 0