A survey was conducted in a college to find out how many

Case Study 1:- A survey was conducted in a college to find out how many students were interested in sports and music. The following table gives the result of the survey.

	Sports Only	Music Only	Both Sports and Music	Neither Sports Nor Music
Boys	40	60	20	30
Girls	30	50	15	35

(i) What is the probability that a student selected at random from the college is interested in sports only ?

(ii) What is the probability that a student selected at random from the college is interested in neither sports nor music ?

What is the probability that a student selected at random from the college is a girl who is interested in music only ?

(iii) What is the probability that a student selected at random from the college is a boy who is interested in either sports or music ?

Solution:-

(i) Total number of boys = 40 + 60 + 20 + 30 = 150

Total number of girls = 30 + 50 + 15 + 35 = 130

∴ Total number of students = 150 + 130 = 280

Let $E_1$ = Event of getting a student interested in sports only.

Then, the number of favourable outcome = 40 + 30 = 70

$P(E_1) = \dfrac{70}{280} = \dfrac{1}{4}$

(ii) Let $E_2$ = Event of getting a student who is interested neither in sports nor music. Then, the number of favourable outcome = 30 + 35 = 65

$P(E_2) = \dfrac{65}{280} = \dfrac{13}{56}$

Let $E_3$ = Event of selecting a boy who is interested in music .

Then, the number of favourable outcome = 50

$P(E_3) = \dfrac{50}{280} = \dfrac{5}{28}$

(iii) Let $E_4$ = Event of selecting a boy who is interseted in sports or music. Then, the number of favourable ourcome = 40 + 60 = 100

$P(E_4) = \dfrac{100}{280} = \dfrac{5}{14}$

Case Study II:- A manufacturer produces two types of TV sets Type A and Type-B. The following table gives the result of a quality control check of a day’s production.

	Type-A	Type-B
Defective	20	30
Non-defective	180	270

(i) What is the probability that a TV set selected at random from the production is defective ?

(ii) If a TV set is defective, what is the probability that it is of Type A ?

If a TV set is non-defective, what is the probability that it is of Type B ?

(iii) If a customer buys a TV set at random, what is the probability that the TV set is of Type B and non-defective ?

Solution:- See full solution

Case Study III:- Eight ball is a game played on pool table with 15 balls numbered 1 to 15 and a “cue ball” that is solid and white. Of the 15 numbered balls, eight are solid(Non white) coloured and numbered 1 to 8 and seven are striped balls balls numbered 9 to 15.

Eight ball is a game played on pool table with 15 balls numbered 1 to 15 and a "cue ball" that is solid and white. Of the 15 numbered balls

The 15 numbered pool balls(No cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random.

Based on the above information, answer the following questions:

(i) What is the probability that the drwn ball bears number 8 ?

(ii) What is the probability that the drwn ball bears an even number ?

What is the probability that the drawn ball bears a number, which is a multiple of 3 ?

(iii) What is the probability that the drawn ball is a solid coloured and bears an even number ?

Solution:- See full solution

Case Study IV:- Ramesh goes to supermarket to purchase soap cartons for his shop. The store has 100 cartons of Moisturizing soap, 150 cartons of Antibacterial soap, 85 cartons of Natural soap and 115 cartons of chemical-free soap. If Ramesh chooses a carton at random, then answer the following questions.

(i) The probability that the selected carton is of moisturizing soap is

(a) 4/9 (b) 7/11

(ii) The probability that the selected carton is not of natural soap is

(a) 14/25 (b) 61/90

(iii) The probability of selecting a carton of chemical-free soap is

(a) 13/90 (b) 15/37

(iv) If the super market storekeeper bought 15 more cartons of anti-bacterial soap, then the probability of selecting a carton of anti-bacterial soap from the super market is

(a) 33/59 (b) 11/31

Solution:- See full solution

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