GPL Mathematical Skills | Probability

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Q. No. 31:	In a charity show tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random (blindly) will have a number with a hundreds digit of 2 ?
A :	0.285
B :	0.40
C :	100/249
D :	99/250

Solution Answer: B 250 numbers between 101 and 350 i.e n(S) = 250 n(E) = 100 digits of 2 = 299-199 = 100 P(E) = n(E)/n(S) = 100/250 = 0.40

Q. No. 32:	A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be :
A :	343/1728
B :	21/36
C :	12/35
D :	7/44

Solution Answer: D Here, n(E) =7_C₁6_C₁5_C₁ And, n(S)= 12_C₁11_C₁10_C₁ P(S) = (765)/(121110) = 7/44

Q. No. 33:	A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd ?
A :	3/8
B :	1/2
C :	3/4
D :	1/8

Solution Answer: B P(odd) = P (even) = 1/2 (because there are 50 odd and 50 even numbers) Sum or the three numbers can be odd only under the following 4 scenarios: Odd + Odd + Odd = 1/2 x 1/2 x 1/2 = 1/8 Odd + Even + Even = 1/2 x 1/2 x 1/2 = 1/8 Even + Odd + Even = 1/2 x 1/2 x 1/2 = 1/8 Even + Even + Odd = 1/2 x 1/2 x 1/2 = 1/8 Other combinations of odd and even will give even numbers. Adding up the 4 scenarios above= 1/8 + 1/8 + 1/8 + 1/8 = 4/8 = 1/2.