Practice Problems on Probability | Class 9 Maths

Probability, in simple words, is the prediction of the happening of an event before it has already happened. We predict many things in our day-to-day lives, like:

• Predict the weather before going for a picnic.
• Predict who is going to win the election.
• Predict the outcome of the toss.

In all these situations we try to find the probability or chances of occurring of an event by considering all the conditions which are in favor of that event. From the above discussion, probability can be defined mathematically as :

Probability is the branch of mathematics that tells us what are the chances for an event to occur. The probability of an event is a number between 0 and 1, where 0 indicates the impossibility of the event and 1 indicates certainty. Therefore, 0 ≤ P(E) ≤ 1, where P(E) = Probability of an event occurring.

Some Basic Terminology used in Probability

Experiment: An experiment is known as an event in which some well-defined outcome is expected.  Also known as sample space. For example, sample space S is S = {H, T}, where H refers to head and T refers to Tail.

Outcome: Outcomes are the results of an experiment. For example, win/loss are possible outcomes of the cricket match.

Impossible Event: When the probability of an event is 0, then the event is known as an impossible event.

Sure Event: When the probability of an event is 1, then the event is known as a sure event.

Probability Formula

The experimental probability or empirical probability of an event is 

Probability(E) = \frac{Number \ of \ favorable \ outcomes}{Total \ number \ of \ outcomes}

Practice Problems on Probability

Question 1: Sumit is playing cricket with his friends, to decide who is going to bat is decided by tossing a coin, whichever wins the toss will bat first. Assuming Sumit and Mohit are captains of the two teams which have chosen heads and tails respectively. Find the chances of Sumit to bat first.

Solution:

We know, there are only two possible outcomes of the toss i.e. heads or tails.

Therefore, Sample space(s) = Total possible outcomes = {H, T}
Sumit needs heads to win the toss, therefore there is only one favorable outcome.
Probability of Sumit to win the toss = favorable outcome / total outcome 
= 1/2 = 0.5

Question 2: Two dice are tossed. Find the probability that the total score is a prime number.

Solution:

Since, two dices are tossed therefore total no of combination = n(S) = (6 x 6) = 36 combinations.

Let us considered E be the event that the sum is a prime number.

All the favorable outcomes are (E) = {(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), 
(2, 3), (2, 5), (3, 2), (3, 4), (4, 1), 
(4, 3), (5, 2), (5, 6), (6, 1), (6, 5)}

Therefore, n(E) = 15
Probability of score to be prime number = n(E)/n(S) = 15/36 = 5/12

Question 3: In a lottery box, there are 10 prizes and 25 blanks. A slip is drawn at random from the lottery box. What is the probability of getting a prize?

Solution:

Given: Total number of prize = 10
Total number of blanks = 25

So, the total number of possible outcomes(i.e., n(S)) are = 10 + 25 = 35

According to the formula
Probability of getting a prize: P(E) = n(E)/n(S) = 1035 = 27

Question 4: A bag contains 8 blue balls and some pink balls. If the probability of drawing a pink ball is half of the probability of drawing a blue ball then find the number of pink balls in the bag.

Solution:

Let us considered the number of pink balls be n.  

The number of blue balls = 8.
Therefore, the total number of balls present in the bag = n + 8.
Now, the probability of drawing a pink ball, i.e. P(X) = n/n + 8
the probability of drawing blue ball, i.e. P(B) = 8/n + 8

According to the question, the probability of drawing pink ball is half of the probability of drawing the blue ball
So, P(X) = P(B)/2
\frac{n}{n+8} = \frac{(\frac{8}{n + 8})}{2}
\frac{n}{n+8} = (\frac{4}{n + 8})
n = 4.

So, number of pink balls present in the bag is 4.

Question 5: Cardsan unmarried workers numbered 1 to 20 are mixed up and then a card is drawn at random. What is the probability that the card drawn has a number which is a multiple of 3 or 5?

Solution:

Card are numbered from 1 to 20 therefore n(S) = {1, 2, 3, 4, ...., 19, 20}.

Let us considered E be the event of getting a multiple of 3 or 5 
So, n(E) = {3, 6, 9, 12, 15, 18, 5, 10, 20}.

According to the formula
P(E) = n(E)/n(S) = 9/20.

Question 6: One card is drawn from a deck of 52 cards, well-shuffled. Calculate the probability that the card will

(i) be an ace,
(ii) not be an ace.

Solution: 

Well-shuffling ensures equally likely outcomes.

(i) There are 4 aces in a deck.
Let us considered E be the event the card drawn is ace.
The number of favorable outcomes to the event E = 4
The number of possible outcomes = 52

Therefore, P(E) = 4/52 = 1/13

(ii) Let us considered F be the event of ‘card is not an ace’
The number of favorable outcomes to F = 52 – 4 = 48
The number of possible outcomes = 52

Therefore, P(F) = 48/52 = 12/13

Question 7: In a simultaneous throw of a pair of dice. Find the probability of getting a total of more than 7.

Solution:

Total number of combinations for a pair of dice is = n(S) = (6 x 6) = 36
Let us considered E be the event of getting a total more than 7
= {(2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), 
(5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Therefore, P(E) = n(E)/n(S) 
= 15/36 = 5/12.

Question 8: In a company of 364 workers, 91 are married. Find the probability of selecting an unmarried worker.

Solution:

Given,
Total workers (i.e. Sample space) = n(S) = 364
Total married workers = 91

Now, total workers who are unmarried = n(E) = 364 – 91 = 273

Method 1: So, the probability of unmarried worker P(NM) = n(E)/n(S) = 273/364 = 0.75
Method 2: P(M) + P(NM) = 1
Here, P(M) = 91/364 = 0.25

So, 0.25 + P(NM) = 1
P(NM) = 1 – 0.25 = 0.75

Question 9: From a bag of yellow and brown balls, the probability of picking a red ball is x/2. Find “x” if the probability of picking a brown ball is 2/3.

Solution:

Given, in the bag only yellow and brown balls.
P(picking a yellow ball) + P(picking a brown ball) = 1

x/2 + 2/3 = 1
3x + 4 = 6
3x = 2
Or, x = 2/3

Question 10: Two coins are tossed simultaneously 360 times. The number of times '2 Tails' appeared was three times the number of times 'No Tail' appeared. Also, the number of times '1 Tail' appeared was twice the number of times 'No Tail' appeared. Find the probability of getting 'Two Tails'.

Solution:

Total number of outcomes = 360
Let us considered the number of times ‘No Tail’ appeared be z
Then, number of times ‘2 Tails’ appeared = 3z
Number of times ‘1 Tail’ appeared = 2z
Now, z + 2z + 3z = 360
6z = 360
z = 60

Hence, the probability of getting 'two tails' = (3 x 60)/360 = 1 /2

Unsolved Practice Problems on Probability

Question 1: A bag contains 5 red balls, 7 blue balls, and 8 green balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:
a) Red?
b) Blue?
c) Not green?

Question 2: A die is thrown once. What is the probability of getting:
a) A number less than 4?
b) A number greater than 4?
c) An even number?

Question 3: A deck of 52 cards is shuffled and one card is drawn at random. What is the probability that the card drawn is:
a) A spade?
b) A queen?
c) Neither a king nor a queen?

Question 4: A jar contains 20 marbles, of which 6 are red, 8 are blue, and 6 are white. If one marble is drawn at random, what is the probability that it is:
a) Blue?
b) Not red?
c) White?

Question 5: In a box of chocolates, there are 12 milk chocolates and 8 dark chocolates. If one chocolate is picked randomly, what is the probability that it is:
a) Milk chocolate?
b) Dark chocolate?
c) Not dark chocolate?

Question 6: Two coins are tossed simultaneously. What is the probability of getting:
a) Two heads?
b) At least one head?
c) No heads?

Question 7: A number is chosen at random from the numbers 1 to 20. What is the probability that the number is:
a) A multiple of 3?
b) A prime number?
c) A multiple of both 2 and 5?

Question 8: A bag contains 10 balls numbered from 1 to 10. If a ball is drawn at random, what is the probability that the number on the ball is:
a) An odd number?
b) A multiple of 4?
c) Not a multiple of 2?

Question 9: In a family of three children, what is the probability that:
a) All three are boys?
b) Exactly two are girls?
c) At least one is a girl?

Question 10: A letter is chosen at random from the word "MATHEMATICS". What is the probability that the letter chosen is:
a) A vowel?
b) A consonant?
c) The letter "M"?

Question 11: There are 4 red, 5 blue, and 6 green balls in the bag. What are the chances that a blue ball will be drawn?

Question 12: A single die is rolled. What is the possibility of getting a number greater than 4?

Question 13: A coin is tossed once. What are the chances that it will not rain?

Question 14: A card is drawn from a standard deck of 52 cards. What is the probability that the card is a queen?

Question 15: If the probability of rain. On a given day is 0.3, what is the probability that it does not rain?

Question 16: In a class of 40 students, 15 students like cricket, 12 students like football, and 5 students like both. What is the probability that a randomly selected student likes either cricket or football?

Question 17: A bag contains 3 red, 4 blue, and 5 green marbles. If a marble is drawn at random, replaced, and then the second marble is drawn, what is the probability of both draws being red marbles?

Question 18: A spinner has 8 equal sections numbered 1 through 8. What is the probability of landing on a number that is not a multiple of 3?

Question 19: A group has 20 students, 12 of them are girls. The student who has been chosen is a girl.

Question 20: A box has 3 white and 7 black balls inside it. If one ball is picked at random, then, in this throwing of one ball, what is the probability of it being black?

Answer Key

1. a) 1/4
b) 7/20
c) 3/5

2. a) 1/2
b) 1/3
c) 1/2

3. a) 1/4
b) 1/13
c) 11/13

4. a) 2/5
b) 7/10
c) 3/10

5. a) 3/5
b) 2/5
c) 4/5

6. a) 1/4
b) 3/4
c) 1/4

7. a) 3/10
b) 2/5
c) 1/10

8. a) 1/2
b) 1/5
c) 1/2

9. a) 1/8
b) 3/8
c) 7/8

10. a) 4/11
b) 7/11
c) 2/11

11. 1/3
12. 1/3
13. 1/2
14. 1/13
15. 0.7
16. 11/20
17. 1/16
18. 5/8
19. 12/20 = 3/5
20. 7/10

Related Articles:

• Probability and Statistics
• Basic Concepts of Probability
• Probability Formulas