Probability

d

just use PIE

c

a

just make fucking cases and calc prob for each of them

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c

4 points divide the circle into 4 parts

let number of people in between be x1, x2, x3, x4

Thus x1 + x2 + x3 + x4 = 16

as x1>= 2, x1 = x1’ + 2

Thus, sigma xi’ = 8

number of soln = 11c3

hence ans is a

actual ans is b

A

d

a

find probabilities that when you get head the first time, the coin is biased and fair

then bias*1/3 + fair*1/2 is the ans

c

we cant control where the alphabets come, but to maximise our chances, we need to ensure that in 6 spins, we get 3As, 2 Bs and 1 O

thus x = 1/6

y = 1/2

z= 1/3

ans is b

c

D(5)/ total number of ways = D(5)/5!

ans b

a,c

a,b

a,c

just make cases

for even, take till n=2 and prob = 1

for odd, till n=3 gives same result in both a,b

so go till n=5 and you’ll get prob = 0.5

a,b,c,d

whenever it loses balls, it loses them in the same ratio as M:N-M

thus, the % of white balls doesnt change

a,d

a,b,c

a,b,c,d

a,c,d

b

39 a

40 d

41 d

42 d

43 c

44 bc

45 a,b,d