Mathematics solution NCERT
Class 9 - Chapter 7: The mathematics of maybe: Introduction to Probability
Q1: A teacher mixes a large bag of sweets of different colours and
randomly selects a sample of 30 sweets. She counts the number of
sweets of each colour:
10 red sweets | 8 green sweets | 7 yellow sweets | 5 blue sweets
(i) Calculate the probability that a randomly picked sweet from
the sample is green.
(ii) If there are 600 sweets in total in the large bag, estimate how
many are likely to be yellow, based on the sample results.
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: A survey is conducted at a school where a random sample of 40
students is asked about their favourite club. The responses are:
14 students: Science Club | 11 students: Arts Club |
9 students: Sports Club | 6 students: Debate Club
Assume there are 800 students in the whole school.
(i) What is the probability that a randomly chosen student from
the sample prefers the Arts Club?
(ii) Using the sample results, estimate how many students in the
whole school are likely to prefer the Sports Club.
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 and record the result each time (heads or tails).
(i) How many times did you get heads?
(ii) How many times did you get tails?
(iii) Calculate the experimental probability of getting heads.
(iv) If you toss the coin once more, what is the probability of
getting tails?
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: Toss a paper cup into the air 100 times. After each toss record whether the cup lands on its bottom, upside down on its top or on its side (See Fig. 7.5). Assign probabilities to the outcomes by using experimental probability.
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: What is the probability of getting an even number when rolling a fair 6-sided 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: Suppose you roll a 6-sided die 12 times and get a ‘3’ three times.
(i) What is the experimental probability of rolling a ‘3’?
(ii) What is the theoretical probability of rolling a ‘3’?
(iii) Why might these probabilities be different? What would you
expect to happen if you roll the die 60, 600, or 6000 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).