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Probability - General Aptitude

Q1:

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

A
1
22

B
3
22

C
2
91

D
2
77

ANS:C -

2
91

Let S be the sample space.

Then, n(S) = number of ways of drawing 3 balls out of 15
= 15C3
= (15 x 14 x 13)
(3 x 2 x 1)
= 455.
Let E = event of getting all the 3 red balls.
n(E) = 5C3 = 5C2 = (5 x 4) = 10.
(2 x 1)
P(E) = n(E) = 10 = 2 .
n(S) 455 91