### Chapter 26 Data Handling IV (Probability) – Exercise 26.1 | Set 1

**Question 11. A bag contains 4 red, 5 black and 6 white balls. One ball is drawn from the bag at random. Find the probability that the ball drawn is:**

**(i) white**

**Solution:**

Number of red balls = 4

Number of black balls = 5

Number of white balls = 6

Total number of balls = 4 + 5 + 6 = 15

Probability of getting a white ball = Favorable outcomes/Total outcomes

= 6/15

= 2/5

Therefore, probability of getting a white ball is 2/5

**(ii)** **Red**

**Solution:**

Number of red balls = 4

Number of black balls = 5

Number of white balls = 6

Total number of balls = 4 + 5 + 6 = 15

Probability of getting a red ball = Favorable outcomes/Total outcomes

= 4/15

Therefore, probability of getting a white ball is 4/15

**(iii)** **Not black**

**Solution:**

Number of red balls = 4

Number of black balls = 5

Number of white balls = 6

Total number of balls = 4 + 5 + 6 = 15

Number of non-black balls = 4 + 6 = 10

Probability of getting a non-black ball = Favorable outcomes/Total outcomes

= 10/15

= 2/3

Therefore, probability of getting a non-black ball is 2/3

**(iv)** **Red or white**

**Solution:**

Number of red balls = 4

Number of black balls = 5

Number of white balls = 6

Total number of balls = 4 + 5 + 6 = 15

Number of red and white balls = 4 + 6 = 10

Probability of getting a red or white ball = Favorable outcomes/Total outcomes

= 10/15

= 2/3

Therefore, probability of getting a red or white ball is 2/3

**Question 12. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:**

**(i)** **Red**

**Solution:**

Number of red balls = 3

Number of black balls = 5

Total number of balls = 3 + 5 = 8

Probability of getting a red ball is = Favorable outcomes/Total outcomes

= 3/8

Therefore, probability of getting a red ball is 3/8

**(ii)** **Black**

**Solution:**

Number of red balls = 3

Number of black balls = 5

Total number of balls = 3 + 5 = 8

Probability of getting a black ball = Favorable outcomes/Total outcomes

= 5/8

Therefore, probability of getting a black ball is 5/8

**Question 13. A bag contains 5 red marbles, 8 white marbles, 4 green marbles. What is the probability that if one marble is taken out of the bag at random, it will be**

**(i) Red**

**Solution:**

Number of red marbles = 5

Number of white marbles = 8

Number of green marbles = 4

Total number of marbles = 5 + 8 + 4 = 17

Probability of getting a red marble = Favorable outcomes/Total outcomes

= 5/17

Therefore, probability of getting a red marble is 5/17

**(ii)** **White**

**Solution:**

Number of red marbles = 5

Number of white marbles = 8

Number of green marbles = 4

Total number of marbles = 5 + 8 + 4 = 17

Probability of getting a white marble = Favorable outcomes/Total outcomes

= 8/17

Therefore, probability of getting a white marble is 8/17

**(iii) Not green**

**Solution:**

Number of red marbles = 5

Number of white marbles = 8

Number of green marbles = 4

Total number of marbles = 5 + 8 + 4 = 17

Total number of non-green marbles = 5 + 8 = 13

Probability of getting a non-green marble = Favorable outcomes/Total outcomes

= 13/17

Therefore, probability of getting a non-green marble is 13/17

**Question 14. If you put 21 consonants and 5 vowels in a bag. What would carry greater probability? Getting a consonant or a vowel? Find each probability?**

**Solution:**

Number of consonants = 21

Number of vowels = 5

Total number of alphabets = 21 + 5 = 26

Probability of getting a consonant is =Favorable outcomes/Total outcomes

= 21/26

Probability of getting a vowel is = Favorable outcomes/Total outcomes

= 5/26

Therefore, the probability of getting a consonant is greater.

**Question 15. If we have 15 boys and 5 girls in a class which carries a higher probability? Getting a copy belonging to a boy or a girl. Can you give it a value?**

**Solution:**

Number of boys = 15

Number of girls = 5

Total number of students = 15 + 5 = 20

Probability of getting a copy of a boy = Favorable outcomes/Total outcomes

= 15/20

= 3/4

Probability of getting a copy of a girl = Favorable outcomes/Total outcomes

= 5/20

= 1/4

Therefore, the probability of getting a copy of a boy is higher.

**Question 16. If you have a collection of 6 pairs of white socks and 3 pairs of black socks. What is the probability that a pair you pick without looking is **

**(i) white?**

**Solution:**

Number of a pair of white socks = 6

Number of a pair of black socks = 3

Total number pairs of socks = 6 + 3 = 9

Probability of getting a white socks = Favorable outcomes/Total outcomes

= 6/9

= 2/3

Therefore, the probability of white socks is 2/3.

**(ii) black?**

**Solution:**

Number of a pair of white socks = 6

Number of a pair of black socks = 3

Total number pairs of socks = 6 + 3 = 9

Probability of getting a black socks = Favorable outcomes/Total outcomes

= 3/9

= 1/3

Therefore, the probability of black socks is 1/3.

**Question 17. If you have a spinning wheel with 3-green sectors, 1-blue sector and 1-red sector. What is the probability of getting a green sector? Is it the maximum?**

**Solution:**

Number of green sectors = 3

Number of blue sector = 1

Number of red sector = 1

Total number of sectors = 3 + 1 + 1 = 5

Probability of getting a green sector = Favorable outcomes/Total outcomes

= 3/5

Probability of getting a blue sector = Favorable outcomes/Total outcomes

= 1/5

Probability of getting a red sector = Favorable outcomes/Total outcomes

= 1/5

Yes, the probability of getting a green sector is maximum.

**Question 18. When two dice are rolled:**

**(i)** **List the outcomes for the event that the total is odd.**

**Solution:**

Possible outcomes when a pair of dice is rolled are

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

Outcomes for the event that the total is odd are (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5)

**(ii)** **Find **the **probability of getting an odd total.**

**Solution:**

Total outcomes = 36

Outcomes for total odd = 18

Probability of getting an event that the total is odd = Favorable outcomes/Total outcomes

= 18/36

= 1/2

Therefore, the probability of getting an odd total is 1/2

**(iii) List the outcomes for the event that total is less than 5.**

**Solution:**

Total outcomes = 36

Outcomes of the event that total is less than 5 are: (1, 1), (1,2), (1,3), (2,1), (2,2), (3,1)

**(iv)** **Find the probability of getting a total less than 5?**

**Solution:**

Total outcomes = 36

Outcomes for total less than 5 = 6

Probability of getting an event that total is less than 5 = Favorable outcomes/Total outcomes

= 6/36

= 1/6

Therefore, the probability of getting an event that total is less than 5 is 1/6

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