Sum of all probabilities =
Ptotal =P(Family, chosen at random has 2 girls) +P(Family, chosen at random has 1 girl) + P(Family, chosen at random has no girl)
= 475/1500 + 814/1500 + 211/1500
= 1500/1500
=1
Must be the result we must get.

The below-written data is representing the blood groups of 30 students study in class VIII.
A, B, O, O, B, A, O, O, AB, O, A, O, B, A, O
A, AB, O, A, A, B, A, B, O, O, O, AB, B, A, O
Total no. of students = 30
Total no. of students of this class who has blood group AB =3
P(Student of this class has blood group AB)= 3/30 => 1/10
Ans: 1/10

The data is representing the concentration of sulfur dioxide in the air in parts per million (ppm) of a city. The data obtained for a month of 30 days is as follows:
Total no. of days =30
No. of days in which Conc. of sulfur dioxide in the interval 0.12 - 0.16 = 2
P(Conc. of sulphur dioxide in the interval 0.12 - 0.16) =2/30
Ans: 1/15

From the above question, the data of our interest is:
Total no. of bags = 11
Total no. of bags that contain more than 5 kg flour = 7
P(Bag contain more than 5 kg flour) = 7/11
Ans: 7/11

This activity can be taken as a general problem:
Well, we know the divisibility by 3 is when the sum of all the digits is divisible by 3
So,
The student will write the number between 100-999
There are 900 3-digit numbers, which are 100, 101, 102, 103, ..., 999.
The first 3-digit numbers that are exactly divisible by 3 is 102, 105, ..... 999
total numbers which are divisible by 3 = 300
P(the...

This activity can be taken as a general problem:
Assumption:
Let the frequency of two-wheelers = x
Let the frequency of three-wheelers = y
Let the frequency of four-wheelers = z
Total no. of vehicles= x+y+z
therefore,
P(anyone vehicle out of the total vehicles I have observed is a two-wheeler) =

Hey, don't you think its too simple:
Well, there is no such engineer whose distance between residence and place of work is less than 1/2 km
Therefore,
engineer whose distance between residence and place of work is less than 1/2 km =0
P(engineer whose distance between residence and place of work is less than 1/2 km) = 0
Ans: 0

Total no. of engineers = 40
Total no. of engineers who are living less than 7 km from their workplace = 31
Therefore we can say,
P(engineers who are living more than or equal to 7 km from their workplace)=31/40
Ans: 31/40

Total no. of engineers = 40
Total no. of engineers who are living less than 7 km from their workplace = 9
Therefore we can say,
P(engineers who are living less than 7 km from their workplace)=
= 9/40
Ans: 9/40

From the above question, the data of our interest is:
Total no. of students =135+65=200
Total no. of students who do not like it.= 65
P(a student does not like it) = 65/200
= 13/40
Ans: 13/40

From the above question, the data of our interest is:
Total no. of students =135+65 =200
Total no. of students who like statistics = 135
P(students like statistics )= 135/200 =27/40
Ans: 27/40

From the above question, the data of our interest is:
Total no. of students =90
Total no. of students who obtained marks 60 or above = 15+8 =23
P(a student obtains marks 60 or above) = 23/90
Ans: 23/90

From the above question, the data of our interest is:
Total no. of students =90
Total no. of students who obtained less than 20% in the mathematics test= 7
P(student obtained less than 20% in the mathematics test) = 7/90
Ans: 7/90

Although it is given that,
Total no. of families= 2400
Let us find by this adding all the cases
= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400
Total number of families owning not more than 1 vehicle= 10+0+1+2+1+160+305+535+469+579 = 2062
Let, P(families owning not more than 1 vehicle)= P5
P5 = 2062/2400

Although it is given that,
Total no. of families= 2400
Let us find by this adding all the cases
= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400
Total number of families,those are earning Rs.13000 – 16000 per month and owning more than 2 vehicles = 25
P(earning Rs.13000 – 16000 per month and owning more than 2 vehicles)= P4
P4 = 25/2400
=1/96
Ans:1/96

Although it is given that,
Total no. of families= 2400
Let us find by this adding all the cases
= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400
Total no. of families, those are earning less than Rs. 7000 per month and not having any vehicle = 10
P(earning less than Rs. 7000 per month and does not have any vehicle)= P3
P3 = 10/2400
=1/240
Ans: 1/240

Although it is given that,
Total no. of families= 2400
Let us find by this adding all the cases
= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400
Total no. of families earning Rs.16000 or more per month and owning exactly 1 vehicle = 579
P(earning Rs.16000 or more per month and owning exactly 1 vehicle )= P2
P2 = 579/2400

Although it is given that,
Total no. of families= 2400
Let us find this by adding all the cases
= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400
Earning Rs. 10000 – Rs.13000 per month and owning exactly 2 vehicles =29
P(Earning Rs. 10000–Rs.13000 per month and owning exactly 2 vehicles)= P1
P1 = 29/2400

Total no. of students = 40
Total no. of students who all are born in August =6
P( a student of the class was born in August) =6/40
=3/20
Ans: 3/20

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