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

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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 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.

Dart Board and Lands in the Interior of the Circle

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 =