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

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Class 10 : Probability

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.

Surface area and Volume Case Study 4:- The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important  monument of India Architecture. It was originally commissioned by the emperor Ashoka in the 3rd century BC. Its nucleus was a simple hemispherical brick structure built over the relics of the Buddha . It is a perfect example of combination of solid figures. A big hemispherical dome with a cuboidal stucture mounted on it. (Take π = 22/7) (i) Calculate the volume of the hemispherical dome if the height of the dome is 21 m.

 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 ?

OR

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 = 280

Let E_1 = event of getting 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}

OR

Let E_3 = event of selecting a girl 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 interested in sports or music. Then, the number of favourable outcome = 40 + 60 = 100

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

Class 10: Probability

Case Study 2:- 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 ?

OR

If a TV set is 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

Surface area and Volume

Case Study 4:- The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important  monument of India Architecture. It was originally commissioned by the emperor Ashoka in the 3rd century BC. Its nucleus was a simple hemispherical brick structure built over the relics of the Buddha . It is a perfect example of combination of solid figures. A big hemispherical dome with a cuboidal stucture mounted on it. (Take π = 22/7)

The Great Stupa at Sanchi is one of the oldest stone structures

(i) Calculate the volume of the hemispherical dome if the height of the dome is 21 m.

Solution:- See full solution

 

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