# NCERT Class 10 Chapter 13 Probability CBSE Board Sample Problems Very Short Answer

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## 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 ¡n 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 =