By using Extra Questions for Class 9 Maths and Ganita Manjari Class 9 Maths Chapter 7 The Mathematics of Maybe Introduction to Probability Extra Questions, students can improve their problem-solving skills.
Class 9 The Mathematics of Maybe Introduction to Probability Extra Questions
Extra Questions on The Mathematics of Maybe Introduction to Probability Class 9
Class 9 Ganita Manjari Chapter 7 Extra Questions
The Mathematics of Maybe Introduction to Probability Class 9 Very Short Question Answer
Question 1.
A and B are the only two outcomes of an event. Probability P(A) = 0.72 then what will be the probability P(B) and why?
Solution:
P(A) + P(B) = 1
∵ Sum of the probabilities of all the outcomes of an event is 1
⇒ 0.72 + P(B) = 1
⇒ P(B)= 1 – 0.72 = 0.28.
Question 2.
Out of the past 250 consecutive days, its weather forecasts were correct 175 times.
(i) What is the probability that on a given day it was correct?
(ii) What is the probability that it was not correct on a given day?
Solution:
Total number of days = 250
(i) Number of days on which the weather forecasts were correct = 175
Probability that on a given day it was correct
= \(\frac{175}{250}=\frac{7}{10}\)
(ii) Probability that it was not correct on a given day = 1 – \(\frac{7}{10}=\frac{3}{10}\)
Question 3.
A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is
(i) black
(ii) not green.
Solution:
In the bag,
number of red balls = 5 number of white balls = 8 number of green balls = 4 number of black balls = 7
Total number of balls in the bag = 5 + 8 + 4 + 7 = 24
(i) Number of black balls = 7
Probability that the ball drawn is black = \(\frac{7}{24}\)
(ii) Number of balls that are not green
= 5 + 8 + 7 = 20
Probability that the ball drawn is not green
= \(\frac{20}{24}=\frac{5}{6}\)
Question 4.
On a particular day, the number of vehicles passing through a crossing is given below:
A particular vehicle is chosen at random. What is the probability that it is not a four-wheeler?
Solution:
Number of two wheelers = 57
Number of three wheelers = 33
Number of four wheelers = 30
Total number of vehicles = 57 + 33 + 30= 120
Number of vehicles that is not a four-wheeler = 57 + 33 = 90
∴ Probability that the vehicle chosen at random is not a four-wheeler = \(\frac{90}{120}=\frac{3}{4}\)
Question 5.
An insurance company selected 1600 drivers at random in a particular city to find a relationship between age and number of accidents. The data obtained are given in the following table:
Find the number of drivers
(a) in the age of 25—40 years and has more than 2 accidents in the year.
(b) the age is above 40 years and has accidents more than 1 but less than 3.
Solution:
(a) The number of drivers in the age of 25-40 years and has more than 2 accidents in the year = 15 + 10 = 25
(b) The number of drivers the age of whose is 40 years and has accidents more than 1 but less than 3 = 13 + 17 = 30.
Question 6.
The king, queen and jack of clubs are removed from a deck of 52 cards and then well shuffled. One card is selected at random from the remaining cards. Find the probability of getting
(a) a heart
(b) a king
(c) the 10 of hearts.
Solution:
Total number of cards in the deck when king, queen and jack of clubs are removed = 52 – 3 = 49
(a) Number of cards which are ‘a heart’ = 13
∴ Probability of getting a heart = \(\frac{13}{49}\)
(b) Number of cards which are ‘a king’ = 3
∴ Probability ot getting a king = \(\frac{3}{49}\)
(c) Number of cards which are ‘the 10 of heart’ = 1
∴ Probability of getting ‘the 10 of hearts’ = \(\frac{1}{49}\)
The Mathematics of Maybe Introduction to Probability Class 9 Short Question Answer
Question 1.
A survey of500 families was conducted to know their opinion about a particular detergent powder. If 375 families liked the detergent powder and the remaining families disliked it, find the probability that a family chosen at random
(i) likes the detergent powder
(ii) does not like it.
Solution:
Total number of families = 500
(i) Number of families who like the detergent powder = 375
∴ Probability that a family chosen at random likes the detergent powder
= \(\frac{375}{500}=\frac{3}{4}\)
(ii) Number of families who dislike the detergent powder = 500-375 =125
∴ Probability that a family chosen at random does not like the detergent powder
= \(\frac{125}{500}=\frac{1}{4}\)
Question 2.
1500 families with 2 children were released randomly and the following data was recorded:
If a family is chosen at random, find the probability that it has
(i) at most one girl
(ii) at least one girl
Solution:
Total number of families = 1500
(i) at most one girl means 0 girl or 1 girl.
Number of families which have at most one girl
= 211 + 814 = 1015
∴ Probability that it has at most one girl
= \(\frac{1015}{1500}=\frac{203}{300}\)
(ii) At least one girl means 1 girls or 2 girls.
Number of families which have at least one girl
= 814 + 475 = 1289
∴ Probability that it has at least one girl
= \(\frac{1289}{1500}\)
Question 3.
A die is rolled 25 times and outcomes are recorded as under:
It is thrown one more time. Find the probability of getting
(a) an even number
(b) a multiple of 3
(c) a prime number.
Solution:
Total number of times a die is rolled = 25
(a) Even numbers are 2, 4, 6.
∴ Probability o f getting an even number = \(\frac{4+6+0}{25}=\frac{10}{25}=\frac{2}{5}\)
(b) Multiples of 3 are 3, 6.
∴ Probability of getting a multiple of 3
= \(\frac{5+0}{25}=\frac{5}{25}=\frac{1}{5}\)
(c) 2, 3, 5 are prime numbers.
∴ Probability of getting a prime number
= \(\frac{4+5+1}{25}=\frac{10}{25}=\frac{2}{5}\)
The Mathematics of Maybe Introduction to Probability Class 9 Long Question Answer
Question 1.
Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is
(a) a number less than 14
(b) a number which is a perfect square
(c) a prime number less than 20.
Solution:
Total number of cards in the box = 100
(a) Numbers less than 14 are
2, 3,4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Their number = 12
∴ Probability that the number on the card is a number less than 14
= \(\frac{12}{100}=\frac{3}{25}\)
(b) Perfect square numbers are
4, 9, 16, 25, 36, 49, 64, 81, 100
Their number = 9
∴ Probability that the number on the card is a number which is a perfect square = \(\frac{9}{100}\)
(c) Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19
Their number = 8
Probability that the number in the card is a 8 2
prime number less than 20 = \(\frac{8}{100}=\frac{2}{25}\).
Question 2.
30 plants were planted in each school out of 12 schools. After a month the number of plants that survived are given below:
What is the probability of survival of
(i) more than 20 plants in a school?
(ii) less than 10 plants in a school?
(iii) exactly 22 plants in a school?
Solution:
Total number of schools = 12
(i) Number of schools in which more than 20 plants survived = 5
∴ Probability of survival of more than 20 plants in a school = \(\frac{5}{12}\)
(ii) Number of schools in which less than 10 plants survived = 1
Probability of survival of less than 10 plants in a school = \(\frac{1}{12}\)
(iii) Number of schools in which exactly 22 plants survived = 2
∴ Probability of survival of exactly 22 plants in a school = \(\frac{2}{12}=\frac{1}{6}\).
Question 3.
The percentages of marks obtained by a student in examination arc given below:
Find the probability that the student gets
(i) a first class i.e. at least 60% marks
(ii) a distinction i.e. 75% or above
(iii) marks between 70% and 80%.
Solution:
Total number of subjects = 5
(i) Number of subjects in which the student gets a first class = 4
Probability that the students gets a first class = \(\frac{4}{5}\)
(ii) Number of subjects in which the student gets a distinction = 2
Probability that the student gets a distinction = \(\frac{2}{5}\)
(iii) Number of subjects in which the student gets marks between 70% and 80% = 2
Probability that the students gets marks between 70% and 80% = \(\frac{2}{5}\).
Question 4.
At a hospital, a doctor compiled the following data about 400 patients whom he could cure of hepatitis:
Another case of hepatitis is reported. What is the probability that this patient will be cured in
(i) less than 2 months?
(ii) 1 month or more but not more than 3 months’.’
Solution:
Total number of patients = 400
(i) Number of patients who were cured in less than 2 months = 210 + 105 = 315
Probability that the patient will be cured in less than 2 months = \(\frac{315}{400}=\frac{63}{80}\)
(ii) Number of patients who were cured in 1 month or more but not more than 3 months = 105 + 60 = 165
Probability that the patient will be cured in 1 month or more but not more than 3 months
= \(\frac{165}{400}=\frac{33}{80}\)
Question 5.
On a busy road, following data was observed about cars passing through it and number of occupants
Suppose another car passes by. Find the chance that it has
(i) exactly 5 occupants
(ii) more than 2 occupants
(iii) less than 5 occupants.
Solution:
Total number of cars
= 29 + 26 + 23 + 17 + 5 = 100
(i) Number of cars having exactly 5 occupants = 5
Probability that it has exactly 5 occupants
= \(\frac{5}{100}=\frac{1}{20}\)
(ii) Number of cars having more than 2 occupants
= 23 + 17 + 5 = 45
Probability that it has more than 2 occupants
= \(\frac{45}{100}=\frac{9}{20}\)
(iii) Number of cars having less than 5 occupants
= 29 + 26 + 23 +17 = 95
Probability that it has less than 5 occupants
= \(\frac{95}{100}=\frac{19}{20}\)
The Mathematics of Maybe Introduction to Probability Class 9 Case Based Questions
A card is drawn at random from a well-shuffled deck of 52 cards.
Question 1.
Find the probability of drawing a king.
Solution:
Kings = 4, Probability = 4/52 = 1/13
Question 2.
Find the probability of drawing a red card.
Solution:
Red cards = 26, Probability = 26/52 = 1/2
Question 3.
Find the probability of drawing a black face card.
Solution:
Black face cards = 6 Probability = 6/52 = 3/26
Question 4.
Is the probability of drawing a joker equal to 0? Explain.
Solution:
Yes, probability of drawing a joker = 0 (since jokers are not part of the standard 52-card deck).
The Mathematics of Maybe Introduction to Probability Extra Questions for Practice
Very Short Answer Type Questions
Question 1.
Write down the sample space S and its size n (S’) for each of the following:
(i) When two fair coins are tossed simultaneously.
(ii) When two unbiased dice are rolled together.
(iii) When two children are chosen at random from a group of 3 boys and 2 girls.
Solution:
(i) S = {HH, HT, TH, TT}; n(S) = 4
(ii) S = {(1, 1), (1, 2), ………. (1, 6); (2, 1), (2, 2), …………, (2, 6); (3, 1) (3, 2), ………. (3, 6); …………….; (6, 1), (6, 2), …………. (6, 6)}; n(S) = 36
(iii) S = {(B1, B2), (B1, B3), (B2, B3), (G1, G2</sub), (B1, G1), (B1, G2)(B2, G1), (B2, G2), (B3, G1), (B3, G2)}; n(S) = 10
Question 2.
A bag contains 14 red and 10 blue balls. Find the probability that a ball drawn from the bag at random is blue.
Solution:
\(\frac{5}{12}\)
Question 3.
In a school of 1250 students, 760 are boys and the remaining are girls. Find the probability that a student selected at random is a girl.
Solution:
\(\frac{49}{125}\)
Question 4.
A coin is tossed 300 times and the following outcomes are recorded:
Head : 165
Tail : 135
Determine the experimental probability of each outcome.
Solution:
\(\frac{11}{20} ; \frac{9}{20}\)
Question 5.
A die is rolled 50 times. It lands on a 4 exactly 8 times. Find the experimental probability of rolling a 4.
Solution:
\(\frac{8}{50}\) or \(\frac{4}{25}\)
Short Answer Type Questions
Question 1.
In a village fair, there are 3 popular sacks available : Samosa, Pakora and Bhaji. For drinks, villagers can choose either Chai or Lassi.
(i) List the sample space of all possible snack and drink combinations a person could choose at the fair.
(ii) List the event “Selecting Samosa as a snack”.
Solution:
(i) Sample space = {(Samosa, Chai), (Samosa, Lassi), (Pakora, Chai), (Pakora, Lassi), (Bhaji, Chai), (Bhaji, Lassi)}
(ii) Event : {(Samosa, Chai), (Samosa, Lassi)}
Question 2.
Prem throws a pair of 6 – sided dice . Write down an event that has a probability of 0 and an outcome that has a probability of 1.
Solution:
(i) Event that has a probability of 0 : The sum of the two numbers that appeared on the two dice is greater than 12.
(ii) Outcome that has a probability of l : The sum of the two numbers that appeared on the two dice is 2 to 12.
Question 3.
Two dice are rolled together. Find the probability that the sum is a prime number greater than 5.
Solution:
\(\frac{2}{9}\)
Question 4.
A bag contains 4 red, 3 green and 2 blue balls. Two balls are drawn without replacement. Find the probability that none is a red ball.
Solution:
\(\frac{5}{18}\)
Long Answer Type Questions
Question 1.
Three coins are tossed. Find the probability that the first coin shows head and exactly two heads occur in total.
Solution:
\(\frac{1}{4}\)
Question 2.
A student takes a multiple-choice test with 3 questions, each having 4 options (A, B, C, D), with only one correct answer. Find the probability that the student guesses and gets exactly 2 anwers correct.
Solution:
\(\frac{9}{64}\)
Case Study Based Questions
A die is rolled twice.
Question 1.
Write the total number of possible outcomes.
Solution:
Total outcomes = 6 x 6 = 36
Question 2.
Find the probability of getting a doublet (same number on both dice).
Solution:
Doublets = {1, 1; 2, 2; 3, 3; 4, 4; 5, 5; 6, 6} → 6 outcomes → Probability = \(\frac{6}{36}=\frac{1}{6}\)
Question 3.
Find the probability of getting a sum greater than 10.
Solution:
Sum > 10 → {5, 6; 6, 5; 6, 6; 4, 6; 6, 4} etc. → 6 outcomes → Probability = \(\frac{6}{36}=\frac{1}{6}\)
Question 4.
Find the probability of getting a prime number on the first die.
Solution:
\(\frac{1}{2}\)