Question

A teacher conducted a survey for 180 students of class 10 for a mathematics project to be given in the class.

She asked the students two MCQ questions, which were "What is their favourite subject?" and "What time do they use their mobile phone at night?". Each student could choose only one option from the choices given below.

The following are the results of the survey conducted:

Mobile phone use	Favourite subject
	Mathematics	Science	Computer	English
Before 9 pm	20	12	8	4
9 pm - 10 pm	13	15	5	8
10 pm - 11 pm	15	18	6	10
After 11 pm	22	10	6	8

Based on the above information, answer the following questions:

1. If a student is selected at random, what is the probability that the student uses mobile phone after 11 pm and that their favourite subject is Mathematics?
2. If a student is selected at random, what is the probability that the student uses mobile phone after 10 pm?
3. If a student is selected at random, what is the probability that their favourite subject is Science?
4. If a student is selected at random, what is the probability that the student uses mobile phone before 10 pm and that their favourite subject is either Mathematics or Computer?

Answer 1

Total number of students = 180.

By formula,

Probability of an event = \[\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\]

i. Number of students who use mobile phone after 11 pm and whose favourite subject is Mathematics = 22.

∴ Required probability = \[\frac{22}{180} = \frac{11}{90}\]

Hence, the required probability = \[\frac{11}{90}\]

ii. Students who use mobile phone after 10 pm = (10 pm - 11 pm) + (After 11 pm)

\[{} = (15 + 18 + 6 + 10) + (22 + 10 + 6 + 8)\]

\[{} = 49 + 46 = 95\]

∴ Required probability = \[\frac{95}{180} = \frac{19}{36}\]

Hence, the required probability = \[\frac{19}{36}\]

iii. Number of students whose favourite subject is Science = \[12 + 15 + 18 + 10 = 55.\]

∴ Required probability = \[\frac{55}{180} = \frac{11}{36}\]

Hence, the required probability = \[\frac{11}{36}\]

iv. Students who use mobile phone before 10 pm are those in the rows ‘Before 9 pm’ and ‘9 pm - 10 pm’.

Number of such students whose favourite subject is Mathematics or Computer 

= (20 + 8) + (13 + 5)

= 28 + 18 = 46.

∴ Required probability = \[\frac{46}{180} = \frac{23}{90}\]

Hence, the required probability = \[\frac{23}{90}\]