There are 20 white hats and 13 black hats in a box. Neeraj randomaly took 3 hats (in succession) out of the box and did not put them in the box. All three hats were black. What is the probability that the fourth hat that he takes out at random will also be black?
Number of white hats = 20
Number of black hats = 13
Total avavilable hats = 33
After removing 3 black hats, number of black hats = 10
Now total available hats = 30
So the probability of took black hat = 10/30 = 1/3
A man died after having a total life of 22476 days.If his date of birth is 17 July 1861.Then his expire date would be ( consider that the total value of a year is 365 days and 6 hrs)
OPtion
1) 4 june 1923
2) 3 july 1923
3) 29 jan 1923
4) 13 feb 1923
5) 15 feb 1923
6) 4 june 1922
7) 3 july 1922
8) 29 jan 1922
9) 13 feb 1922
10) None of the above
Solution
22476 days = 61 years (including 15 leap years of 366 days) + 196 days
Total days in the year 1861 counted from 17 july = 168
Remaining days = 28
so it would be 29 jan 1923
3 points are required to form a triangle so no. of triangles formed = 10*9*8/3*2*1 = 120
but out of these points 4 are in a line so rejected methods are 4*3*2/3*2*1 = 4
answer = 120-4 = 116
When two dice are thrown total number of results can be obtained are 36.
Hence n(S) = 36
Event of getting total of 7 or 9 are { (6, 1), (5, 2), (4, 3), (6, 3), (5, 4)}
Hence n( E) = 5
So, PE = n(E)/n(S) = 5/36
The age of a Mohan is three times the sum of the ages of his two sons. Five years hence, his age will be double of the sum of the ages of his sons. The father's present age is?
Let the sum of ages of two sons be x years
Age of man = 3xyears
After 5 years age of the man =(3x+5) years
Sum of ages of two sons =(x+10) years
Given, (3x+5) =2(x+10)
⇒ (3x+5) =2x+20
⇒ x=15
Hence 3x=3(15) = 45
∴ Present age of father is 45years.
A number is increased by 70 % and then decreased by 70 %. Find the net increase or decrease per cent.
OPtion
1) 56%
2) 25%
3) 35%
4) 46%
5) 48%
6) 49%
7) 53%
8) 52%
9) No change
10) None of the above
Solution
A number is increased by 70 % and then decreased by 70 %. Find the net increase or decrease per cent.
Let the number be 100.
Increase in the number = 70 % = 40 % of 100
= (40/100 × 100)
= 70
Therefore, increased number = 100 + 70 = 170
This number is decreased by 70 %
Therefore, decrease in number = 70 % of 170
= (70/100 × 170)
= 11900/100
= 119
Therefore, new number = 170 - 119 = 51
Thus, net decreases = 100 - 51 = 49
Hence, net percentage decrease = (49/100 × 100)
= (4900/100)
= 49 %
Five players for a cricket team is to be selected from 4 Batsman, 3 Bowlers and 2 All Rounders. In how many ways can the committee be formed If the Committee should consist of 2 Batsman, 2 Bowler and 1 All-rounder?