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.

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 =