SBI Associate PO 2010

Total number of students in R = 2000

Percentage of girls = 28%

So, the number of boys = .72 * 2000 = 1440

Total number of students in U = 1000

Percentage of girls = 15%

So, the number of boys = .85 * 1000 = 850

So, the percentage of boys = $$ \frac{850+1440}{2000+1000}$$* 100

= 76.33%

Total students in T = 1250

Percentage of girls = 40%

So, the number of boys = 1250 * .6 = 750

The number of students in R = 2000

The approximate number of students in S = 2250

So, the required percentage = 100 * 2000/2250 = 89%

Total number of students in P = 2500

Percentage of girls = 40%

So, the number of boys = .60 * 2500 = 1500

Total number of students in Q = 3000

Percentage of girls = 45%

So, the number of boys = .55 * 3000 = 1650

So, the average = (1500 + 1650)/2 = 1575

Total number of students in P = 2500

Percentage of girls = 40%

So, the number of girls = .40 * 2500 = 1000

Total number of students in Q = 3000

Percentage of girls = 45%

So, the number of girls = .45 * 3000 = 1350

So, the ratio = 1000 : 1350 = 100 : 135 = 20 : 27

The total number of ways of picking three marbles from the given 12 marbles is $$^{12}C_3 = 220$$

The number of ways of picking three green marbles is $$^3C_3 = 1$$
The number of ways of picking three red marbles is $$^4C_3 = 4$$
Hence, the total number of favorable cases is $$4+1 = 5$$

Hence, the required probability is $$\frac{5}{220} = \frac{1}{44}$$

The total number of ways of picking two marbles is $$^{12}C_2 = 66$$

The total number of ways of picking two red marbles is $$^4C_2 = 6$$

Hence, the required probability is $$\frac{6}{66} = \frac{1}{11}$$

The total number of ways of picking three marbles is $$^{12}C_3 = 220$$

The total number of ways of picking three marbles such that none of them is blue (that is all of them are either red or green) is $$^7C_3 = 35$$

Hence, the number of favorable cases (atleast one is blue) is $$220 - 35 = 185$$

So, the required probability is $$\frac{185}{220} = \frac{37}{44}$$

A committee with all 4 professors and and 1 research associate can be formed in 6 ways as any 1 of 6 Research Associates can be selected.

A committee with all 3 trainees and 2 professors can be formed in 6 ways as 2 professors out of 4 can be selected in 4C2 ways.

Hence a desired committee can be formed in 12 ways.

2 trainees out of 3 can be chosen in 3C2 = 3 ways.

3 research associates out of 6 can be chosen in 6C3 = 20 ways.

A committee with 2 trainees and 3 research associates can be formed in 3*20 = 60 ways.