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  #81  
Old Saturday, January 28, 2017
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Default Complete Solution of 12(a)

Data:
Total Events/Sample Space/No. of People = 1000
People having Blood Group A = 300
People having Blood Group B = 325
People having Blood Group O = 250
People having Blood Group AB = 125

Solution:
Probability of having Blood Group AB = People having Blood Group AB / Total Number of People

Probability of having Blood Group AB = 125/1000
Probability of having Blood Group AB = 0.125
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  #82  
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Default Complete Solution of 12(b)

Data:
Persons = 5
Ahmad, Ali, Akbar, Nasir and Shehbaz

Cities = 5
V, W, X, Y and Z

Modes of Transport = 5
Bus, Train, Aeroplane, Car and Boat

Scenario:

Person Mode of Transport City
Akbar Car Y
Ali Aeroplane X
Nasir Boat
Shehbaz Train

Bus ≠ X, W
Boat ≠ X

So,
The remaining mode of transport is now Bus
and the remaining person is Ahmad
so, Ahmad must traveled by Bus
and
Remaining Cities are X, W and Z

Therefore,
Person Mode of Transport City
Akbar Car Y
Ali Aeroplane X
Nasir Boat
Shehbaz Train
Ahmad Bus

As there is no Bus Service towards X and W.
So, there is two possibilities which are:

#1
Person Mode of Transport City

Akbar Car Y
Ali Aeroplane X
Nasir Boat W
Shehbaz Train
Ahmad Bus

#2
Person Mode of Transport City

Akbar Car Y
Ali Aeroplane X
Nasir Boat
Shehbaz Train W
Ahmad Bus

So, Now There is two further possibilities of each case (#1 and #2) having total of 4 possibilities or scenario

#1
[Possibility 1]
Person Mode of Transport City

Akbar Car Y
Ali Aeroplane X
Nasir Boat W
Shehbaz Train V
Ahmad Bus Z

#1
[Possibility 2]
Person Mode of Transport City

Akbar Car Y
Ali Aeroplane X
Nasir Boat W
Shehbaz Train Z
Ahmad Bus V

#2
[Possibility 3]
Person Mode of Transport City

Akbar Car Y
Ali Aeroplane X
Nasir Boat V
Shehbaz Train W
Ahmad Bus Z

#2
[Possibility 4]
Person Mode of Transport City

Akbar Car Y
Ali Aeroplane X
Nasir Boat Z
Shehbaz Train W
Ahmad Bus V

Questions:
i. How did Ahmed travel and where did he go?
So, by viewing these 4 Possibilities
Ahmed must traveled through Bus to either go to the City V or Z.

ii. Which mode of transport was used by the person who traveled to X city?
In every possibility
Ali traveled through Aeroplane to reach the city X.
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  #83  
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Default Complete Solution of 12(b)

Data:
Persons = 5
Ahmad, Ali, Akbar, Nasir and Shehbaz

Cities = 5
V, W, X, Y and Z

Modes of Transport = 5
Bus, Train, Aeroplane, Car and Boat

Scenario:

Person : Mode of Transport : City

Akbar : Car : Y
Ali : Aeroplane : X
Nasir : Boat :
Shehbaz : Train :

Bus ≠ X, W
Boat ≠ X

So,
The remaining mode of transport is now Bus
and the remaining person is Ahmad
so, Ahmad must traveled by Bus
and
Remaining Cities are X, W and Z

Therefore,
Person : Mode of Transport : City
Akbar : Car : Y
Ali : Aeroplane : X
Nasir : Boat :
Shehbaz : Train :
Ahmad : Bus :

As there is no Bus Service towards X and W.
So, there is two possibilities which are:

#1
Person : Mode of Transport : City

Akbar : Car : Y
Ali : Aeroplane : X
Nasir : Boat : W
Shehbaz : Train :
Ahmad : Bus :

#2
Person : Mode of Transport : City

Akbar : Car : Y
Ali : Aeroplane : X
Nasir : Boat :
Shehbaz : Train : W
Ahmad : Bus :

So, Now There is two further possibilities of each case (#1 and #2) having total of 4 possibilities or scenario

#1
[Possibility 1]
Person : Mode of Transport : City

Akbar : Car : Y
Ali : Aeroplane : X
Nasir : Boat : W
Shehbaz : Train : V
Ahmad : Bus : Z

#1
[Possibility 2]
Person : Mode of Transport : City

Akbar : Car : Y
Ali : Aeroplane : X
Nasir : Boat : W
Shehbaz : Train : Z
Ahmad : Bus : V

#2
[Possibility 3]
Person : Mode of Transport : City

Akbar : Car : Y
Ali : Aeroplane : X
Nasir : Boat : V
Shehbaz : Train : W
Ahmad : Bus : Z

#2
[Possibility 4]
Person : Mode of Transport : City

Akbar : Car : Y
Ali : Aeroplane : X
Nasir : Boat : Z
Shehbaz : Train : W
Ahmad : Bus : V

Questions:
i. How did Ahmed travel and where did he go?

So, by viewing these 4 Possibilities
Ahmed must traveled through Bus to either go to the City V or Z.

ii. Which mode of transport was used by the person who traveled to X city?
In every possibility
Ali traveled through Aeroplane to reach the city X.
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  #84  
Old Saturday, January 28, 2017
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Default Complete Solution of 11(a)

(i) How many stores does the distribution company serve?
Total Number of stores = 3+15+26+20+16=80

(ii) What is the most common distance of stores from the company's godown?
For this always see maximum frequency which is 26 in this table/case:
So,
The most common distance of stores from the company's godown is 21 to 30 kilometers (because it has the maximum frequency; 26 stores).

(iii) How many stores are 35 km or more from the godown?
From Table:
There are 16 stores which are 41 km or more from the godown, and 20 stores which are between 31 to 40 km from the godown. From the table we cannot say anything that how many of these 20 stores are 35 km or more from the godown.

(iv) What percentage of stores are 31 km or more from the godown?
There are 20+16=36 stores which are 31 km or more from the godown. Hence, the percentage of these stores is given as,
36/Total no. of stores = 36/80 = 0.45
0.45 x 100%
45%
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  #85  
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Default Complete Solution of 10(b)

Data:
15, 15, 16, 16, 16, 17, 17, 18, 19

Solution:
The mean is defined as, the sum of the values divided by the number of values.
The mean of the above data set is given as,
=15+15+16+16+16+17+17+18+19/9
=149/9
=16.556

Median:
The middle value of an arranged data set is called median.
Arranged data means writing the values in ascending order. The given values in ascending order are given as:
15, 15, 16, 16, 16, 17, 17, 18, 19 (already in ascending order)
Hence, the median of the above data set is given as
15+15+16+16+16+17+17+18+19
Median = 16

Mode:
The mode is the most repeated value in a data set.
The most repeated value in the given data is 16.
So, Mode = 16

Range:
Range is the difference between the largest value and the smallest value.
In the given data set the largest value is 19, and the smallest value is 15. Hence,
Range = 19 − 15 = 4
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  #86  
Old Monday, January 28, 2019
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