Class-9 Maths Chapter-15 Probability

 Class 9 Maths 

Chapter 15 Probability  

Question 1.In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

Solution: Here, the total number of trials = 30
∵ Number of times, the ball touched the boundary =6
∴ Number of times, the ball missed the boundary = 30 – 6 = 24
Let the event of not hitting the boundary be represented by E, then
P(E)=[No.oftimesthebatswomandidnothittheboundary][Totalnumberofballssheplayed]=2430=45
Thus, the required probability = 45

Question 2.1500 families with 2 children were selected randomly, and the following data were recorded

Compute the probability of a family, chosen at random, having
(i) 2 girls
(ii) 1 girl
(iii) no girl
Also, check whether the sum of these probabilities is 1.

Solution:Here, total number of families = 1500

(i) ∵ Number of families having 2 girls = 475
∴ Probability of selecting a family having 2 girls = 4751500=1960

(ii) ∵ Number of families having 1 girl = 814
∴ Probability of selecting a family having 1 girl = 8141500=407750

(iii) Number of families having no girl = 211
Probability of selecting a family having no girl = 2111500
Now, the sum of the obtained probabilities
=1960+407750+2111500=475+814+2111500=15001500=1
i.e., Sum of the above probabilities is 1.

Question 3.In a particular section of class IX, 40 students were asked about the month of their birth and the following graph was prepared for the data so obtained.

Find the probability that a student of the class was born in August.

Solution:From the graph, we have
Total number of students bom in various months = 40
Number of students bom in August = 6
∴ Probability of a student of the Class-IX who was bom in August =640+320

Question 4.Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes.

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Solution:Total number of times the three coins are tossed = 200
Number of outcomes in which 2 heads coming up = 72
∴ Probability of 2 heads coming up = 72200=925
∴ Thus, the required probability = 925

Question 5.An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below.

Suppose a family is chosen. Find the probability that the family chosen is
(i) earning ₹ 10000-13000 per month and owning exactly 2 vehicles.
(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than ₹ 7000 per month and does not own any vehicle.
(iv) earning ₹13000-16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.

Solution:Here, total number of families = 2400
(i) ∵ Number of families earning Rs. 10000 – Rs. 13000 per month and owning exactly 2 vehicles = 29
∴ Probability of a family earning Rs. 10000 – Rs. 13000 per month and owning exactly 2 vehicles = 292400

(ii) ∵ Number of families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579
∴ Probability of a family earning Rs. 16000 or more per month and owning exactly 1 vehicle = 5792400

(iii) ∵ Number of families earning less than Rs. 7000 per month and do not own any vehicle = 10
∴ Probability of a family earning less than Rs. 7000 per month and does not own any vehicle = 102400 = 1240

(iv) ∵ Number of families earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles = 25
∴ Probability of a family earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles = 252400 = 196

(v) ∵ Number of families owning not more than 1 vehicle
= [Number of families having no vehicle] + [Number of families having only 1 vehicle]
= [10 + 1 + 2 + 1] + [160 + 305 + 535 + 469 + 579] = 14 + 2048 = 2062
∴ Probability of a family owning not more than 1 vehicle = 20622400 = 10311200

Question 6.A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows
0 – 20, 20 – 30, …, 60 – 70, 70 – 100. Then she formed the following table

(i) Find the probability that a student obtained less than 20% in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.

Solution:Total number of students = 90
(i) From the given table, number of students who obtained less than 20% marks = 7
Probability of a student obtaining less than 20% marks = 790

(ii) From the given table, number of students who obtained marks 60 or above = [Number of students in class-interval 60 – 70] + [Number of students in the class interval 70 – above]
= 15 + 8 = 23
∴ Probability of a student who obtained 23 marks 60 or above = 2390

Question 7.To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table

Find the probability that a student chosen at random
(i) likes statistics,
(ii) does not like it.

Solution:Total number of students whose opinion is obtained = 200
(i) ∵ Number of students who like statistics = 135
∴ Probability of selecting a student who likes statistics = 135200 = 2740

(ii) ∵ Number of students who do not like statistics = 65
∴ Probability of selecting a student who does not like statistics = 60200 = 1340

Question 8.The distance (in km) of 40 engineers from their residence to their place of work were found as follows

What is the empirical probability that an engineer lives
(i) less than 7 km from her place of work?
(ii) more than or equal to 7 km from her place of work?
(iii) within 12 km from her place of work?

Solution:Here, total number of engineers = 40

(i) ∵ Number of engineers who are living less than 7 km from their work place = 9
∴ Probability of an engineer who is living less than 7 km from her place of work = 940

(ii) ∵ Number of engineers living at a distance more than or equal to 7 km from their work place = 31
∴ Probability of an engineer who is living at distance more than or equal to 7 km from her place of work = 3140

(iii) ∵ The number of engineers living within 12km from their work place = 0
∴ Probability of an engineer who is living within 12km from her place of work = 040 = 0

Question 11.Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg)

4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00
Find the probability that any of these bags,chosen at random contains more than 5 kg of flour.

Solution:Here, total number of bags = 11
∵ Number of bags having more than 5 kg of flour = 7
∴ Probability of a bag having more than 5 kg of flour = 711

CLASS-9 ENGLISH-CHAPTER RAIN ON THE ROOF

English Poem
Chapter 
Rain On The Roof

 

Thinking about the poem

Question 1.What do the following phrases mean to you? Discuss in class.

1.     Humid shadows: These are the shadows of different things which become wet during the rainy season.

2.     Starry spheres: The area where stars appear in a group in the sky.

3.     What a bliss: The poet feels happy when he listens to the rain drops.

4.     A thousand dreamy fancies into busy being start: The poet starts recollecting the past and finds himself lost in reveries and dreams in the rainy weather.

5.     A thousand recollections weave their air-threads into woof: The poet recollects hundreds of memories in the rainy season. They weave a weft with the help of air-threads.

Question 2.What does the poet like to do when it rains?
Answer:When it rains the poet wants to lie on bed in a cottage and listen to pitter-patter sound of the rain.

Question 3.What is the single major memory that comes to the poet’s mind? Who are the “darling dreamers” he refers to?
Answer:The poet’s mother is the single major memory that comes to his mind. ‘Darling dreamers’ are those ‘kids’ who remember their mothers like the poet.

Question 4.Is the poet now a child? Is his mother still alive?
Answer:No, the poet is not a child. His mother is no more. But her memories still haunt him.

II.Answer these questions:-

Question 1.When you were a young child, did your mother tuck you in, as the poet’s mother did?
Answer:Yes, my mother used to tuck me in when I was a child. Whenever I said that I could not do some work, she embraced me and took me in her lap to get that work done. She used to feel sad and dejected if I was involved in any mishap.

Question 2.Do you like rain? What do you do when it rains steadily or heavily as described in the poem?
Answer:Yes, I like rain and prefer to take a bath in the rain for some time. But when it rains heavily, I stay inside and enjoy the beauty of nature

Question 3.Does everybody have a cosy bed to lie in when it rains? Look around you and describe how different kinds of people or animals spend time, seek shelter, etc. during rain.
Answer:No, everybody is not so fortunate to have a cosy bed to lie in when it rains. There are some people who live at the railway platforms and bus terminal. They don’t have even bed sheet, what to talk of comfortable beds

III.Short answer type questions

Question 1.What is a ‘bliss’ for a poet in the poem?
Answer:The poet loves rain because it carries him in old memories. He thinks it is bliss to hear the sound of the rain on the roof. He lies in his cozy bed and enjoys the music of nature. It is a bliss for him.

Question 2.What shows that the poet loved his mother?
Answer:The poet loved his mother. He remembered her when he lied on his cozy bed to enjoy the sound of rain. It appeared to him as if she was fondly looking at him.

Question 3.When does the ‘thousand dream fancies’ begin to weave in the poet’s mind?

Answer:When the poet is in his cottage and lies in his cozy bed listening to the soft music of rain on the roof, himind is flooded with memories of his mother. He recalls his childhood.

class-8 Computer chapter-4 Inserting Images and Creating lists in HTML

Chapter-4  

Inserting Images and Creating lists in HTML

 

Answer the following Questions:-
Que-1  What is an <IMG> tag? Name its Attributes.
Ans-1  An <IMG> tag is used to insert image in webpage.

Que-2What is the difference between Ordered and unordered Lists?
Ans-2 A numbered or a list of proper order is known as an ordered list.
A list that is in no specific order is known as an unordered list.

Que-3Exaplain the align attribute of the <IMG> tag.
Ans-3 The align attribute is used when aligning the image with respect to the margins or the inline texts.<IMG align=center>

Que-4 What do you mean by a nested list?
Ans-4 There will be times you would want to form multilevel lists. To make ordered and unordered lists are nested together which are known as nested lists.

Que-5 What does the alt attribute of the <IMG> tag do?
Ans-5 If the image is not able be displayed a text in its place , it will be displayed.