Mathematics solution NCERT
Class 9 - Chapter 7: The mathematics of maybe: Introduction to Probability
Q1: Sweets in a Bag
Given:
- Red sweets = 10
- Green sweets = 8
- Yellow sweets = 7
- Blue sweets = 5
Total sweets in sample:
10 + 8 + 7 + 5 = 30
(i) Probability that a randomly picked sweet is green
P(Green) = Number of green sweets / Total sweets
= 8/30
= 4/15
Answer: 4/15
(ii) Estimate the number of yellow sweets in a bag of 600 sweets
Fraction of yellow sweets = 7/30
Estimated yellow sweets = (7/30) × 600
= 140
Answer: 140 yellow sweets
Q2: Favourite Club Survey
Given:
| Club | Students |
|---|---|
| Science Club | 14 |
| Arts Club | 11 |
| Sports Club | 9 |
| Debate Club | 6 |
Total students surveyed = 40
Total school strength = 800
(i) Probability that a randomly chosen student prefers Arts Club
P(Arts Club) = 11/40
Answer: 11/40
(ii) Estimate the number of students who prefer Sports Club
Sports Club fraction = 9/40
Estimated number = (9/40) × 800
= 180
Answer: 180 students
Q3: Toss a Coin 20 Times
This activity depends on the actual results obtained by the student.
One possible set of results is shown below.
| Outcome | Frequency |
|---|---|
| Heads | 11 |
| Tails | 9 |
(i) Number of heads
11
(ii) Number of tails
9
(iii) Experimental probability of getting heads
= 11/20
= 0.55
Answer: 11/20
(iv) Probability of getting tails on the next toss
A fair coin has:
P(Tails) = 1/2
Answer: 1/2
Q4: Tossing a Paper Cup
This is an experimental activity. Results may differ.
Suppose after 100 tosses we get:
| Position | Frequency |
|---|---|
| Bottom | 35 |
| Top | 20 |
| Side | 45 |
Total tosses = 100
Experimental Probabilities
| Outcome | Probability |
|---|---|
| Bottom | 35/100 = 0.35 |
| Top | 20/100 = 0.20 |
| Side | 45/100 = 0.45 |
Q5: Probability of Getting an Even Number on a Fair Die
Possible outcomes:
{1, 2, 3, 4, 5, 6}
Even numbers:
{2, 4, 6}
Number of favourable outcomes = 3
Total outcomes = 6
P(Even Number) = 3/6 = 1/2
Answer: 1/2
Q6: Rolling a Die 12 Times
Given:
Number 3 appeared 3 times in 12 rolls.
(i) Experimental Probability of rolling a 3
= 3/12
= 1/4
Answer: 1/4
(ii) Theoretical Probability of rolling a 3
= 1/6
Answer: 1/6
(iii) Why are these probabilities different?
Experimental probability is based on a small number of actual trials, while theoretical probability is based on all equally likely outcomes.
With only 12 rolls, results may differ from the theoretical value.
As the number of rolls increases to 60, 600, or 6000, the experimental probability will get closer and closer to 1/6.
Answer:
For a very large number of rolls, the experimental probability approaches the theoretical probability (1/6).