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 x 3C1
Required probability = 4C2 x 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 %
No comments:
Post a Comment