### DATA ANALYSIS & INTERPRETATION

DATA ANALYSIS AND ITERPRETATION

Problems  based on Combinations & Probability !

Problem – An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles.
Two marbles are picked randomly. What is the probability that both are red.
a.      1/6
b.      1/3
c.      2/15
d.      2/5
e.      None
Answer – First one ball can be picked out of six and next time one out of five. So total ways of pick 2 red = 6C2 = 6! / ( 4! X 2! ) = 15
Total number of picking any two balls =  15C2 = 105
P(R) = 6C2 / 15C2 = 15 / 105 = 1/7

Problem – If three marbles are picked randomly what is the probability that two are blue and one is yellow.
a.      3/91
b.      1/5
c.      18/455
d.      7/15
e.      None
Answer – Picking three balls, total number of exhaustive cases = 15C3
Picking three balls, in required fashion = 4C2   3C1
Required probability =  4C2   3C1   15C3 = 6 x 3 / 455  = 18 / 455

Problem – If four marbles are picked at random, then what is the probability that atleast one is blue.
a.      4/15
b.      69/91
c.      11/15
d.      22/91
e.      None
Answer – Picking 4, total No of exhaustive cases = 15C4
No of cases when we will have none blue = picking 4 balls from remaining 11 other colour balls = 11C4
If we subtract this from total number of cases we get cases where atleast one ball will be blue
= 15C4  -  11C4  = 1365 – 330 = 1035
Probability = 1035 / 1365 =  207 /273 =69/91
Now you must have understood how to deal with such types.

Problem – Study the table carefully and answer the questions that follow.

 Number of People staying in Five different localities and the % breakup of men, women and chidren Locality Total No of People Percentage Men Women Children F 5640 55 35 10 G 4850 34 44 22 H 5200 48 39 13 I 6020 65 25 10 J 4900 42 41 17

Question – What is the total number of men and children staying together in locality I ?
a.      4115
b.      4515
c.      4551
d.      4155
Answer – Total number of men and children staying together in locality I = ( 65% + 10% )of 6020
=(0.65+0.10) x 6020 = 0.75 x 6020 = 4515

Quesiton – The number of women staying in which locality is highest ?
a.      H
b.      J
c.      F
d.      G
Answer -  Number of women staying in each of these 4 localities are
In H = 39% of 5200 = 0.39 x 5200= 2028
In J = 41% of 4200 = 0.41 x 4200 = 2009
In F = 35% of 5640 = 0.35 x 5640 = 1974
In G = 44% of 4850 = 0.44 x 4850 = 2015
Clearly in H locality there are highest  number of women.

Question – What is the total number of children staying together in ,locality H & I together ?
a.      1287
b.      1278
c.      1827
d.      1728
Answer -  Number of children in H = 13% of 5200 = 0.13 x 5200 = 676
Number of Children in I = 10% of 6020 = 0.10 x 6020 = 602
Total number of children staying together in I &H  locality together  = 676 + 602 = 1278

Question -   The total number of people staying in locality J forms what percentage of total number of people staying in locality F ?
a.      81
b.      72
c.      78
d.      93
e.      87
Answer -  People in locality J divded by people in locality F = 4900 / 5640 =  0.8687 0.87 or 87 %