Probability Question 105
Question: Three integers are chosen at random from the first 20 integers. The probability that their product is even, is
[Kurukshetra CEE 2002]
Options:
A) $ \frac{2}{19} $
B) $ \frac{3}{29} $
C) $ \frac{17}{19} $
D) $ \frac{4}{19} $
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Answer:
Correct Answer: C
Solution:
The total number of ways in which 3 integers can be chosen from first 20 integers is $ ^{20}C_3. $
The product of three integers will be even if at least one of them is even.
$ \therefore $ Required probability = 1 ? Probability that none is even $ =1-\frac{^{10}C_3}{^{20}C_3}=1-\frac{2}{19}=\frac{17}{19}. $
BETA
