Class 9 The Mathematics of Maybe: Introduction to Probability

📌 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)=Number of favourable outcomesTotal number of outcomes\text{Probability (P)} = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}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