**KSEEB SSLC Solutions for Class 10 Maths – Probability (English Medium)**

**Exercise 5.1:**

**Question 1:**

A fair die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:

Outcome |
1 | 2 | 3 | 4 | 5 | 6 |

Frequency |
179 | 150 | 157 | 149 | 175 | 190 |

Find the probability of getting each outcome.

**Solution :**

**Question 2:**

An insurance company selected 2000 drivers (without any preference of one driver over another) to find a relationship between age and accidents. The data obtained are given in the following table:

Age of drivers (in years) |
Accidents in one year |
||||

0 | 1 | 2 | 3 | Over 3 | |

18 – 29 | 440 | 160 | 110 | 61 | 35 |

30 – 50 | 505 | 125 | 60 | 22 | 18 |

Above 50 | 360 | 45 | 35 | 15 | 09 |

Find the probabilities of the following events.

- Being 18-29 years of age and having exactly 3 accidents in one year.
- Being 30-50 years of age and having one or more accidents in a year.
- Being above 50 years of age and having no accidents in one year.

**Solution :**

**Question 3:**

The blood group of 30 students in a class are recorded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. Find the probability that a student of this class selected at random has blood group AB. (Hint: write the frequencies for each type of blood group)

**Solution :**

The frequencies for each group is shown below:

Blood group |
Number of students |

A | 9 |

B | 6 |

AB | 3 |

O | 12 |

Total | 30 |

Question 4:

To know the opinion of the students about the subject music, a survey of 200 students was conducted. The data is recorded in the following table.

Opinion |
Number of students |

Like | 135 |

Dislike | 65 |

Find the probability that a student chosen at random

(i) like it

(ii) does not like it.

**Solution :**

**Question 5:**

A survey of 850 working women showed that 158 used own four-wheeler to commute to the work place, 416 used two wheeler and the remaining public transport. Out of these women, if one is chosen randomly, what is the probability that the women commutes by

(i) own four wheeler

(ii) two wheeler

(iii) public transport.

**Solution :**

**Question 6:**

A survey of 200 people in a village was conducted and the number of times each person visits the city was observed as shown.

Visit to City |
Once in a month |
Once in a 15 days |
Once in a week |

Frequency |
32 | 128 | 40 |

What is the probability that the randomly selected person visits the city

(i) once in a month

(ii) once in 15 days

(iii) once in a week.

**Solution :**

**Exercise 5.2:**

**Question 1:**

A die is rolled. Find the probability of getting

(i) the number 4

(ii) a square number

(iii) a cube number

(iv) a number greater than 1

**Solution :**

**Question 2:**

Two coins are tossed together. What is the probability of getting

(i) no tail

(ii) at most two tails

(iii) exactly one head

(iv) at least one tail

**Solution :**

**Question 3:**

Three coins are tossed together. Find the probability of getting.

(i) at least one head

(ii) at most two heads

(ii) no head

(iv) all heads

**Solution :**

**Question 4:**

Two dice are thrown together. Find the probability of getting.

(i) a sum equal to 8

(ii) a sum less than 12

(iii) the sum divisible by 4

(iv) a product of 12

(v) a product less than 20

(vi) the product divisible by 5

**Solution :**

**Question 5:**

A number is selected at random from 1 to 50. What is the probability that it is

(i) a prime number

(ii) not a perfect cube

(iii) a perfect square

(iv) a triangular number

(v) a multiple of 6

(vi) not a multiple of 2

**Solution :**

**Question 6:**

One card is drawn randomly from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is

(i) a spade

(ii) a red coloured card

(iii) not a black coloured card

(iv) a queen

(v) not a diamond

(vi) an ace

(vii) not an ace

(viii) a black king

(ix) a red jack

(x) a heart with number less than 10.

**Solution :**

**Question 7:**

A two-digit number is formed with the digits 2, 5 and 7, where repetition of digits is not allowed. Find the probability that the number so formed is

(i) a square number

(ii) divisible by 3

(iii) greater than 52

(iv) less than 57

(v) less than 25

(vi) a whole number

**Solution :**

**Question 8:**

Nine rotten mangoes are mixed with 30 good ones. One mango is chosen at random. What is the probability of choosing a

(i) good mango

(ii) rotten mango

**Solution :**

**Question 9:**

During holi festival, Sonali filled 7 bottles with different coloured water – red, blue, green, pink, yellow, purple and orange.

One bottle is selected at random. What is the probability of choosing the bottle with

(i) orange colour

(ii) not yellow colour

(iii) brown colour

(iv) either red or green

(v) neither yellow or pink

**Solution :**

**Question 10:**

A box contains 144 pens of which 20 are defective and the others are good. A person will buy a pen if it is good and will not buy if it is defective. The shopkeeper draws one pen from the box at random and gives it to the person. What is the probability that the person

(i) will buy it?

(ii) will not buy it?

**Solution :**

**Question 11:**

26 English alphabet cards (without repetition) are put in a box and shuffled well. If a card is chosen at random, find the probability that the letter is

(i) a vowel

(ii) a consonant

(iii) between g and t

(iv) one which comes after p

(v) one which comes before m

**Solution :**

**Question 12:**

The following table shows the blood group of 60 students who donated blood.

Blood Group |
A | B | AB | 0 |

Number of students |
16 | 12 | 9 | 23 |

If one student is chosen at random, what is the probability that the blood group will be

(i) A

(ii) B

(iii) AB

(iv) O

(v) Not B

(vi) Not AB

(vii) A or AB

(viii) B or O

**Solution :**

**Question 13:**

A and B are friends. What is the probability that both will have,

(i) the same birth day

(ii) different birth days (ignore a leap year)

**Solution :**

**Question 14:**

A box contains 12 balls out of which ‘x are red.

(i) If one ball is drawn, what is the probability of getting a red ball?

(ii) If six more red balls are put in the box, the probability of drawing a red ball will be doubled than the earlier. Find ‘x’.

**Solution :**

**Question 15:**

A game consists of rolling two dice. If the sum is 2, 3, 4, 5, 10, 11 or 12, player A wins. If it is 6, 7, 8 or 9, player B wins. Would you rather be player A or B? Explain.

**Solution :**

**Exercise 5.3:**

**Question 1:**

The probability that it will rain on a particular day is 0.64 what is the probability that it will not rain on that day?

**Solution :**

**Question 2:**

**Solution :**

**Question 4:**

**Solution :**

**Question 5:**

**Solution :**

**Question 6:**

Two coins are tossed simultaneously. Find the probability that either both heads or both tails occur.

**Solution :**

When two coins are tossed simultaneously, the sample space is given by

S = {HH, HT, TH, TT}

∴ n(S) = 4

Let A be the event of getting two heads.

A = {HH}

∴ n(A) = 1

**Question 7:**

When a die is thrown, find the probability that either an odd number or a square number occurs.

**Solution :**

When a die is thrown, the sample space is given by

S = {1, 2, 3, 4, 5, 6}

∴ n(S) = 6

Let A be the event of getting an odd number.

A = {1, 3, 5}

∴ n(A) = 3

**Question 8:**

On number card is chosen randomly from the number cards 1 to 25, Find the probability that it is divisible by 3 or 11.

**Solution :**

Sample space, S = {1, 2, 3,…….,25}

∴ n(S) = 25

Let A be the event that the number card chosen is divisible by 3.

A = {3, 6, 9, 12, 15, 18, 21, 24}

∴ n(A) = 8

**Question 9:**

Two dice are thrown simultaneously. Find the probability that the sum of the numbers on the faces is neither divisible by 4 nor by 5.

**Solution :**

**Question 10:**

Two die are thrown together, Find the probability that the product of the numbers on the faces is either divisible by 5 or by 7.

**Solution :**

**Question 11(i):**

A card is drawn from a well-shuffled deck of 52 cards, Find the probability that it will be a diamond or a spade

**Solution :**

**Question 11(ii):**

A card is drawn from a well-shuffled deck of 52 cards, Find the probability that it will be a red coloured card or black coloured card

**Solution :**

**Question 11(iii):**

A card is drawn from a well-shuffled deck of 52 cards, Find the probability that it will be an ace or a jack or a queen.

**Solution :**

**Question 11(iv):**

A card is drawn from a well-shuffled deck of 52 cards, Find the probability that it will be the number 9 or 10 or 8 or 4.

**Solution :**

**Question 12:**

The outcome of a random experiment results in either success or failure. If the probability of success is thrice the probability of failure, find the probability of success.

**Solution :**

Let A be the event that experiment results in success.

And, let B be the event that experiment results in failure.

It is given that

P(A) = 3P(B)

**Exercise 5.4:**

**Question 1:**

There are 2 red and 2 yellow flowers in a basket. A child picks up at random three flowers, What is the probability of picking up both the yellow flowers?

**Solution :**

Total number of flowers = 2 red + 2 yellow = 4

Out of these, 3 flowers can be picked up in ^{4}C_{3} = 4 ways

∴ n(S) = 4

Let A be the event that both the flowers are yellow.

Now, 2 flowers out of 2 yellow flowers can be picked up in ^{2}C_{2} = 1 way

The remaining 1 flower can be picked up from the 2 red flowers in ^{2}C_{1} = 2 ways

∴ n(A) = 1 × 2 = 2

**Question 2:**

Shekar is one member of a group of 5 persons. If 3 out of these 5 persons is to be chosen, for a committee find the probability of Shekar being in the committee.

**Solution :**

Number of persons = 5

Out of these, a committee of 3 can be selected in ^{5}C_{3} ways.

**Question 3:**

Three cards are drawn at random from a pack of 52 cards. What is the probability that all the three cards are kings?

**Solution :**

**Question 4:**

Find the probability that when 7 cards are drawn at random from a well shuffled deck of 52 cards, it contains

(i) all jacks

(ii) three jacks

(iii) at least three jacks.

**Solution :**

**Question 5:**

Three squares of chess board are selected at random. Find the probability of getting two squares of one colour and the other of different colour.

**Solution :**

**Question 6:**

A committee of five persons is selected from 4 men and 3 women. What is the probability that the committee will have

(i) one man

(ii) two men

(iii) two women

(iv) at least two men.

**Solution :**