Probability Question 102
Question: Out of 30 consecutive numbers, 2 are chosen at random. The probability that their sum is odd, is
[Kurukshetra CEE 2002]
Options:
A) $ \frac{14}{29} $
B) $ \frac{16}{29} $
C) $ \frac{15}{29} $
D) $ \frac{10}{29} $
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Answer:
Correct Answer: C
Solution:
The total number of ways in which 2 integers can be chosen from the given 30 integers is $ ^{30}C_2. $ The sum of the selected numbers is odd if exactly one of them is even and one is odd.
Favourable number of outcomes = $ ^{15}C_1{{.}^{15}}C_1 $
$ \therefore $ Required probability $ =\frac{^{15}C_1.{{}^{15}}C_1}{^{30}C_2}=\frac{15}{29} $ .
BETA
