Probability Question 21
Question: If out of 20 consecutive whole numbers two are chosen at random, then the probability that their sum is odd, is
Options:
A) $ \frac{5}{19} $
B) $ \frac{10}{19} $
C) $ \frac{9}{19} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
The total number of ways in which 2 integers can be chosen from the given 20 integers $ {}^{20}C_2. $ The sum of the selected numbers is odd if exactly one of them is given and one is odd.
$ \therefore $ Favourable number of outcomes $ ={}^{10}C_1\times {}^{10}C_1 $
$ \therefore $ Required probability $ =\frac{{}^{10}C_1\times {}^{10}C_1}{{}^{20}C_2}=\frac{10}{19}. $
BETA
