A group of students conducted a survey to find out about the preferred mode of transportation to school among their classmates. They surveyed 200 students from their school. The results of the survey are as follows: 120 students preferred to walk to school. 25% of the students preferred to use bicycles. 10% of the students preferred to take the bus. Remaining students preferred to be dropped off by car. Based on the above information, answer the following questions: (i) What is the probability that a randomly selected student does not prefer to walk to school? (ii) Find the probability of a randomly selected student who prefers to walk or use a bicycle. (iii) (A) One day 50% of walking students decided to come by bicycle. What is the probability that a randomly selected student comes to school using a bicycle on that day? (iii) (B) What is the probability that a randomly selected student prefers to be dropped off by car?

MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 36

From the official CBSE sample question paper for 2024-25, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedProbability

A group of students conducted a survey to find out about the preferred mode of transportation to school among their classmates. They surveyed 200 students from their school. The results of the survey are as follows:

120 students preferred to walk to school.
25% of the students preferred to use bicycles.
10% of the students preferred to take the bus.
Remaining students preferred to be dropped off by car.

Based on the above information, answer the following questions:

(i)
What is the probability that a randomly selected student does not prefer to walk to school?
1 mark
(ii)
Find the probability of a randomly selected student who prefers to walk or use a bicycle.
1 mark
(iii)
(A) One day 50% of walking students decided to come by bicycle. What is the probability that a randomly selected student comes to school using a bicycle on that day?
2 marks
OR
(iii)
(B) What is the probability that a randomly selected student prefers to be dropped off by car?
2 marks

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

Open one hint at a time and try again before the next.

Hint 1

Convert each percentage into a number of students out of 200.

Hint 2

Probability = favourable students ÷ 200; for 'walk or bicycle' add the two groups.

Hint 3

On the special day, add half of the walkers to the bicycle group; car students are whatever is left after walk, bicycle and bus.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

First find the number of students in each group. Walk = 120. Bicycle = $25%$ of $200 = 50$ . Bus = $10%$ of $200 = 20$ . Car = $200 - (120 + 50 + 20) = 10$ .
(i) Students who do not prefer to walk $= 200 - 120 = 80$ .
½ mark
(i) $P (not walk) = \frac{80}{200} = \frac{2}{5}$ .
½ mark
(ii) Students who prefer to walk or use a bicycle $= 120 + 50 = 170$ .
½ mark
(ii) $P (walk or bicycle) = \frac{170}{200} = \frac{17}{20}$ .
½ mark
(iii)(a) Walking students who switch to bicycle $= 50%$ of $120 = 60$ .
½ mark
(iii)(a) Students already using a bicycle $= 50$ , so bicycle users that day $= 60 + 50 = 110$ .
½ mark
(iii)(a) $P (bicycle that day) = \frac{110}{200} = \frac{11}{20}$ .
1 mark
(iii)(b) Students dropped by car $= 200 - (120 + 50 + 20) = 10$ .
1 mark
(iii)(b) $P (car) = \frac{10}{200} = \frac{1}{20}$ .
1 mark

Answer: (i) 2/5; (ii) 17/20; (iii)(A) 11/20; (iii)(B) 1/20

Where the marks are

Finds 80 students who do not walk (½ mark)
Probability $\frac{80}{200} = \frac{2}{5}$ (½ mark)
Finds 170 students who walk or cycle (½ mark)
Probability $\frac{17}{20}$ (½ mark)
(iii)(A): 60 walkers switch to bicycle (½ mark)
(iii)(A): adds the existing 50 to get 110 (½ mark)
(iii)(A): probability $\frac{11}{20}$ (1 mark)
(iii)(B): car students $= 10$ (1 mark)
(iii)(B): probability $\frac{1}{20}$ (1 mark)

Revise the chapter

Chapter: Probability (notes, formulas, where marks are lost and every past question)
Topic: Properties of Probability and Complementary Events

Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 36

Hints

Step-by-step solution

Revise the chapter

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