The Mathematics of Maybe Introduction to Probability Class 9 Worksheet with Answers Maths Chapter 7 - #NCSOLVE 📚

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The Mathematics of Maybe Introduction to Probability Worksheet Class 9

Class 9 Maths The Mathematics of Maybe Introduction to Probability Worksheet

Worksheet On The Mathematics of Maybe Introduction to Probability Class 9

Multiple Choice Questions

Question 1.
In a survey of 500 teenagers, it was found that 125 prefer reading physical books over e-books. If a teenager is selected at random, the probability that he/she prefer physical books is:
(a) 0.25
(b) 0.50
(c) 0.75
(d) 0.80
Answer:
(a) 0.25

Question 2.
In a survey of a housing society, the preferred modes of transport for 100 residents were recorded:

Mode of Transport	Bicycle	Car	Public Bus	Walking
Number of Residents	15	45	32	8

A resident is selected at random. The probability that the resident prefers using a bicycle is:
(a) \(\frac{3}{20}\)
(b) \(\frac{9}{20}\)
(c) \(\frac{8}{25}\)
(d) \(\frac{2}{25}\)
Answer:
(a) \(\frac{3}{20}\)

Question 3.
Three coins are tossed 200 times and the outcomes are recorded as follows:

Number of Tails	3	2	1	0
Frequency	25	50	75	50

Based on this information, the probability of getting at least two heads is:
(a) \(\frac{5}{8}\)
(b) \(\frac{19}{40}\)
(c) \(\frac{21}{40}\)
(d) \(\frac{1}{4}\)
Answer:
(a) \(\frac{5}{8}\)

Question 4.
A box contains 50 light bulbs. They are tested, and their lifespan is recorded. The maximum lifespan found is 1000 hours. One bulb is selected at random. The probability that its life is 1200 hours is:
(a) \(\frac{1}{50}\)
(b) 0
(c) 1
(d) 0.5
Answer:
(b) 0

In Q. 5 to 7, over 300 working days, a machine produced faulty bolts as follows:

Number of Faulty Bolts	0	1	2	3	4	5	6
Days	80	75	60	25	25	10	5

Question 5.
Based on the data, what is the probability that the machine produces exactly 0 faulty bolts on a given day?
(a) \(\frac{8}{300}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{4}{15}\)
(d) 0.80
Answer:
(c) \(\frac{4}{15}\)

Question 6.
What is the probability that the output will have at least 1 faulty bolt?
(a) \(\frac{11}{15}\)
(b) \(\frac{75}{100}\)
(c) \(\frac{4}{15}\)
(d) 0.50
Answer:
(a) \(\frac{11}{15}\)

Question 7.
Calculate the probability that the output has exactly 3 faulty bolts.
(a) 300
(b) 0.45
(c) 0.30
(d) 0.15 E
Answer:
(d) 0.15 E

Question 8.
A fair die is rolled twice. What is the probability that the sum of the two numbers is prime?
(a) \(\frac{18}{36}\)
(b) \(\frac{15}{36}\)
(c) \(\frac{12}{36}\)
(d) \(\frac{21}{36}\)
Answer:
(b) \(\frac{15}{36}\)

Question 9.
In a survey of 500 students, 280 like mathematics, 150 like science, and the remaining like other subjects. If one student is chosen at random, what is the probability that the student likes other subjects?
(a) \(\frac{7}{15}\)
(b) \(\frac{360}{500}\)
(c) \(\frac{280}{500}\)
(d) \(\frac{150}{500}\)
Answer:
(a) \(\frac{7}{15}\)

Question 10.
A batsman hits a boundary 6 times out of 30 balls. If he plays 120 balls in another match, what is the expected number of boundaries?
(a) 18
(b) 24
(c) 22
(d) 20
Answer:
(b) 24

Question 11.
A bag contains 10 balls numbered 1 to 10. One ball is drawn at random. Without directly listing, what is the probability that the number on the ball is not a prime?
(a) \(\frac{4}{10}\)
(b) \(\frac{5}{10}\)
(c) \(\frac{6}{10}\)
(d) \(\frac{7}{10}\)
Answer:
(c) \(\frac{6}{10}\)

Question 12.
A fair die is rolled once. What is the chance that the outcome is a multiple of 2 but not a multiple of 3?
(a) \(\frac{1}{6}\)
(b) \(\frac{2}{6}\)
(c) \(\frac{3}{6}\)
(d) \(\frac{4}{6}\)
Answer:
(b) \(\frac{2}{6}\)

Question 13.
A coin is tossed two times. What is the probability that the number of heads is equal to the number of tails?
(a) \(\frac{1}{2}\)
(b) \(\frac{3}{8}\)
(c) \(\frac{1}{4}\)
(d) None of these
Answer:
(a) \(\frac{1}{2}\)

Question 14.
A bag contains 4 red, 3 blue, and 5 green balls. One ball is drawn at random. What is the probability that the ball is neither red nor green?
(a) \(\frac{1}{6}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{3}\)
(d) \(\frac{2}{3}\)
Answer:
(b) \(\frac{1}{4}\)

Question 15.
A coin is tossed three times. What is the probability that the number of heads is more than the number of tails?
(a) \(\frac{3}{4}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{5}{8}\)
(d) \(\frac{6}{8}\)
Answer:
(b) \(\frac{1}{2}\)

Assertion-Reason

In Q. 1 to 5, two statements are given, one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the options (a), (b), (c), and (d) given below.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.

1. Assertion (A): The probability of getting a prime number when a fair die is rolled once is \(\frac{1}{2}\)
Reason (R): The prime numbers on a die are {2, 3, 5}, which are 3 outcomes out of 6.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

2. Assertion (A): The probability of drawing a red card from a standard deck of 52 cards is \(\frac{1}{2}\)
Reason (R): In a deck, there are 26 red cards (hearts and diamonds) out of 52.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

3. Assertion (A): The probability of picking a vowel from the word “MATHS” is 0.
Reason (R): An event that has a probability of 0 is known as an impossible event.
Answer:
(d) Assertion (A) is false, but Reason (R) is true.

4. Assertion (A): The probability of any event always lies between 0 and 1.
Reason (R): Probability is the ratio of the number of favourable outcomes to the number of total outcomes.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

5. Assertion (A): The probability of an event is 1.12.
Reason (R): The probability P(E) of any event E always satisfies 0 ≤ P(E) ≤ 1.
Answer:
(d) Assertion (A) is false, but Reason (R) is true.

The Mathematics of Maybe Introduction to Probability Class 9 Ganita Manjari Worksheet

Short Answer Type Questions – I

Question 1.
What is the probability of an event that is certain to happen? Give an example.
Answer:
1

Question 2.
A bag contains 4 red balls and 6 blue balls. What is the probability of drawing a red ball?
Answer:
0.4 or \(\frac{4}{10}\) or \(\frac{2}{5}\)

Question 3.
Why can the probability of an event never be -0.5 or 1.2?
Answer:
0 ≤ P(E) ≤ 1

Short Answer Type Questions – II

Question 1.
A box contains 20 numbered cards, numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the card is:
(a) even
(b) multiple of 3.
Answer:
(a) \(\frac{1}{2}\)
(b) \(\frac{3}{10}\)

Question 2.
80 students from a city school were surveyed regarding their primary mode of transport to school. The results are recorded in the table below:

Mode of Transport	School Bus	Private Car	Bicycle	Walking
Number of Students	32	16	20	12

Total students in sample = 80
Total students in the school = 1600

(a) Find the experimental probability that a randomly selected student from the sample prefers to use the school bus.
Answer:
\(\frac{2}{5}\) or 0.4

(b) Using the sample results, estimate the total number of students in the whole school who are likely to prefer bicycles.
Answer:
400 students

Question 3.
A librarian examines a random sample of 50 books returned to the library to check their genre. The findings are recorded as: 15 Fiction, 12 Non-Fiction, 18 Biography, 5 Poetry Calculate the experimental probability that a randomly picked book from the sample is a Biography. If the library has a total of 2000 books, estimate how many are likely to be Fiction, based on the sample results.
Answer:
\(\frac{9}{25}\);600

Question 4.
You have a fair spinner divided into 5 equal sections coloured red, blue, green, yellow and orange. You spin it 20 times and record that it land on ‘red’ exactly 6 times.
(a) What is the experimental as well as theoretical probability of the spinner landing on red?
Answer:
\(\frac{3}{10}\); \(\frac{1}{5}\)

(b) If you increase the number of spins to 500 or 5000, what is expected to be happen?
Answer:
The experimental probability is expected to get closer to the theoretical probability \(\frac{1}{5}\)

Question 5.
A mobile manufacturing company checks 800 units for screen defects. The data is:
Table- 2
Number of defective screens
Frequency (units)
Answer:
One unit is selected at random. Find the probability that it has:
(a) Exactly 3 defective screens
(b) Between 1 and 4 defective screens (inclusive)
(c) No defective screens
Answer:
(a) \(\frac{1}{20}\)
(b) \(\frac{53}{160}\)
(c) \(\frac{13}{20}\)

Question 5.
A mall surveyed 250 customers.

Age Group (years)	10-19	20-29	30-39	40-49	50+
Number of Customers	45	70	65	50	20

Find the probability that a selected customer is:
(a) Under 30 years
(b) 40 years or more
Answer:
(a) \(\frac{23}{50}\)
(b) \(\frac{7}{25}\)

Activity

Question 1.
Take two fair 6-sided dice. Roll them simultaneously. Write the sample space for this experiment. Also, find the probability that the sum of the numbers appearing on the top faces of the dice is a perfect square.
Answer:
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} 1;\(\frac{7}{36}\)

Long Answer Type Questions

Question 1.
In a game, a player spins a spinner divided into 3 equal sectors colored Red, Blue, and Yellow. After the . spinner stops, the player tosses a fair coin.
(a) Draw a tree diagram to show all possible outcomes of the spinner and the coin.
(b) List all the outcomes in the sample space.
(c) What is the probability of the spinner landing on Red and the coin showing Heads?
Answer:
(b) S = {(Red, Heads), ( Red, Tails), (Blue, Heads), (Blue, Tails), (Yellow, Heads), (Yellow, Tails)}
(c) \(\frac{1}{6}\)

Question 2.
A student rolls a die and then tosses a coin,
(a) Write the sample space.
(b) Find the probability of getting an even number and a tail.
(c) Find the probability of getting a number less than 3 and a head.
Answes:
(a) S = [{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{6}\)

Question 3.
In a school election with 250 voters, students were asked to state their preferences for a Student Leader and a Club. The data collected are given below:
Club Preference among voters for Candidate X: Sports (90), Arts (60)
Club Preference among voters for Candidate Y: Sports (30), Arts (70)
(a) Construct a tree diagram to represent the election preference flow.
(b) Find the probability that a randomly selected voter chose “Sports” as his/her preference.
(c) If there are 1,000 students in the school, how many are estimated to choose Candidate X and Arts, based on the sample results?
Answer:
(b) \(\frac{12}{25}\)
(c) 240

Case Based Questions

Question 1.
A school canteen offers a “Healthy Combo” where a student must pick one main item from basket A and one drink from basket B. Basket A contains 1 Veg Wrap (W) and 2 Cheese Sandwiches (S₁; S₂). Basket B contains 1 Lemonade (L) and 1 Fresh Juice (J).
Based on the above information, answer the following questions.
(a) Draw a tree diagram representing all possible combo outcomes.
Answer:

(b) Find the probability that a student picks a cheese sandwich and a fresh juice.
Answer:
\(\frac{1}{3}\)

(c) What is the probability that the combo includes a veg wrap?
Answer:
\(\frac{1}{3}\)

OR
Calculate the probability that the drink selected is lemonade.
Answer:
\(\frac{1}{2}\)

Question 2.
A glass jar contains 3 Red marbles (R) and 2 Blue marbles (B). A student conducts an experiment where he picks one marble, record its colour, put it back, and then pick a second marble.
Based on the above information, answer the following questions.
(a) Construct a tree diagram illustrating the possible outcomes for both draws.

(b) What is the probability that both marbles picked are of the same colour?
Answer:
\(\frac{13}{25}\)

(c) Find the probability that at least one Red marble is picked.
Answer:
\(\frac{21}{25}\)
OR
What is the probability that the first marble is Blue and the second is Red?
Answer:
\(\frac{6}{25}\)

Competency Based Questions

Question 1.
Write the sample space and calculate the probability for each case.
(a) Two coins are tossed at the same time. Find the probability of getting at least one heads.
Answer:
\(\frac{3}{4}\)

(b) A bag contains 3 red, 2 blue, and 1 green ball. One ball is picked. Find the probability that it is not red.
Answer:
\(\frac{1}{2}\)

(c) Three coins are tossed. Find the probability of getting exactly two heads.
Answer:
\(\frac{3}{8}\)

Question 2.
Two fair 6-sided dice are rolled simultaneously. Calculate the probability that:
(a) the sum of the numbers is a multiple of 4.
(b) the product of the numbers is a perfect square.
Answer:
(a) \(\frac{1}{4}\)
(b) \(\frac{4}{18}\)

Question 3.
Electricity usage of 2000 households is recorded.

Consumption (Units)	0-100	101-200	201-300	301-400	above 400
Number of Households	300	700	600	300	100

Find the probability that a randomly selected household:
(a) uses at most 200 units
(b) uses more than 300 units
Answer:
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{5}\)

The post The Mathematics of Maybe Introduction to Probability Class 9 Worksheet with Answers Maths Chapter 7 appeared first on Learn CBSE.

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