Class 10: Probability
Case Study 5:- “Eight Ball” is a game played on a 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 striped balls numbered 9 to 15.
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 drawn ball bears number 8?
(ii) What is the probability that the drawn ball bears an even number ?
OR
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:-
(i) Total number of balls = 15
Number of ball bears numbers 8 = 1
P(Drawing a ball bears number 8) = 1/15
(ii) Even number balls are 2, 4, 6, 8, 10, 12 and 14
Total number of even balls = 7
P(Drawing a ball bears an even number) = 7/15
OR
Number of ball bears a number which is a multiple of 3 are3, 6, 9, 12 and 15
∴ Total number of ball bears a number, which is a multiple of 3 = 5
P(Drawing a ball bears a number having a multiple of 3) = 5/15
(iii) Number of solid coloured balls = 8
Number of solid coloured balls having an even number = 4
P(Drawing a solid coloured and bears an even number ball) = 4/15
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 ?
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:- See full solution
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
Case Study 3:- Ramesh goes to supermarket to puchase 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 then answer the following question.
(i) The probability that the selected carton is of moisturizing soap is
(a) 4/9 (b) 7/11
(c) 3/13 (d) 2/9
(ii) The probability that the selected carton is not of natural soap is
(a) 14/25 (b) 61/90
(c) 73/90 (d) None of these
(iii) The probability of selecting a carton of chemical free soap is
(a) 13/90 (b) 15/37
(c) 16/31 (d) 23/90
(iv) If the Supermarket storekeeper bought 15 more cartones 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
(c) 75/101 (d) None of these
Solution:- See full solution
Case Study 4:- Spinning wheel game are popular activity at birthday parties. They are a fun and easy way to add some excitement to the party, and they can be enjoyed by people of all ages. There are many different spinning wheel game that can be played at a birthday party.
Spin the wheel and win a prize: This is a simple game where the players spins the wheel and then wins a prize that the wheel lands on. The prizes can be anything from small toys to candy to gift cards.
Rohit organized his birthday party and invited all his friend for the same. He also arranges the game Spin the wheel and wins aprize for fun. On the basis of the above information, answer the following the question.
(i) If Ashok spins the wheel, then find the probability that he get a cricket kit.
(ii) If Anita spins the wheel, then the probability of getting no prize.
OR
If Anshu spins the wheel, then find the probability that the wheel stops at soccer ball.
(iii) Find the probability of winning a volley ball.
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)
(i) Calculate the volume of the hemispherical dome if the height of the dome is 21 m.
Solution:- See full solution