# NCERT Class 10 Chapter 13 Probability CBSE Board Sample Problems Very Short Answer (For CBSE, ICSE, IAS, NET, NRA 2023)

Glide to success with Doorsteptutor material for CBSE/Class-10 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-10.

## Question

A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.

### Solution

Total English alphabets = 26

Number of consonants in English alphabets = 21

P (Choosing a consonant)

## Question

20 tickets, on which numbers 1 to 20 are written, are mixed thoroughly and then a ticket is drawn at random out of them. Find the probability that the number on the drawn ticket is a multiple of 3 or 7.

### Solution

When one ticket is drawn, total possible cases are 20.

Favourable cases when the number is a multiple of 3 or 7 are 3, 6, 9, 12, 15, 18,7, 14, i.e.. 8 cases.

Required probability

## Question

A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

### Solution

Number of total possible outcomes when one card is drawn = 52

Number of favourable outcomes when card is neither red nor queen = 28

Required probability

## Question

Cards marked with number 3, 4,5, 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected card bears a perfect square number.

### Solution

Total possible outcomes when one card is drawn

When the number on drawn card is a perfect square, total favourable cases are 4,9, 16,

25,36, 49, i.e.. = 6

P (perfect square number)

## Question

In the adjoining figure a dart is thrown at the dart board and lands in the interior of the circle. What is the probability that the dart will land in the shaded region.

### Solution

We have

and

Using Pythagoras Theorem in , we have

[O is the midpoint of Ad

Area of the circle sq. units

sq. units

Area of shaded region = Area of the circle - Area of rectangle ABCD

Area of shaded region sq. unit.

Hence

P (Dart lands in the shaded region) =

## Question

A number x is selected from the numbers 1,2, 3 and then a second number y is randomly selected from the numbers 1,4, 9, what is the probability that the product xy of the two numbers will be less than 9?

### Solution

Number x can be selected in three ways and corresponding to each such way there are three ways of selecting number y. Therefore, two numbers can be selected in 9 ways as listed below:

Favourable number of elementary events

Hence, required probability

## Question

An integer is chosen at random from the first two hundreds digit. What is the probability that the integer chosen is divisible by 6 or 8?

### Solution

Multiples of 6 first 200 integers

6,12, 18, 24, 30,36, 42, 48, 54,60, 66, 72, 78,84, 90, 96, 102,108, 114, 120, 126,132, 138, 144, 150,156, 162, 168, 174,180, 186, 192, 198

Multiples of 8 first 200 integers

8,16, 24, 32,40, 48, 56,64, 72, 80,88, 96, 104,112, 120, 128,136, 144, 152,160, 168, 176,184, 192, 200

Number of Multiples of 6 or

P (Multiples of 6 or 8)

## Question

An integer is chosen between 70 and 100, Find the probability that it is

i) A prime number

ii) Divisible by 7

### Solution

Total number of integers

Prime numbers between 70 and 100 are

Probability (Prime number)

Numbers between 70 and 100 divisible by 7 are

Probability (number divisible by 7)

## Question

Jayanti throws a pair of dice and records the product of the numbers appearing on the dice. Pihu throws 1 dice and records the squares the number that appears on it. Who has the better chance of getting the number 36? Justify?

### Solution

For jayanti,

Favourable outcome is i. e1

Probability (getting the number 36) =

For Pihu,

Favourable outcome is 6 i.e.. , 1

Probability (getting the number 36) =

Pihu has the better chance.

## Question

If two coins are tossed simultaneously. Find the probability of getting 2 heads.

### Solution

Sample space for tossing two coins is S

Let E = event of getting 2 heads

Favourable outcome

Total outcome = 4

## Question

A lot of 25 bulbs contain 5 defective ones. One bulb is drawn at random from the lot.

What is the probability that the bulb is good?

### Solution

Total number of bulbs

No. of bulbs defective

No. of good bulbs

P (good bulb) =

## Question

A die is rolled, Find the probability of getting a factor of 6.

### Solution

The factors of 6 are 1,2, 3,6

So the probability of getting a factor of 6 is =

## Question

There are 5 blue, 6 red and 7 green balls in a bag. If a ball is picked up at random, what is the probability of getting a non-blue ball?

### Solution

The probability of getting a non-blue ball is

## Question

Find the probability of having 53 Sundays in an ordinary year

### Solution

An ordinary year has 365 days.

52 weeks and 1 extra day

52 weeks have 52 Sundays

Year will have 53 Sundays if and only if the extra day is a Sunday.

P of having 53 Sundays =