First slide

Theorems of probability

Question

Three integers are chosen at random from the first 20 integers. The probability that their product is even, is

Easy

A

_{$\frac{2}{19}$}
B

_{$\frac{3}{29}$}
C

_{$\frac{17}{19}$}
D

_{$\frac{4}{29}$}

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 the integers is even. Therefore, the required probability
$= 1 -$ probability that none of three integers is even $= 1 - \frac{10_{C_{3}}}{20_{C_{3}}} = 1 - \frac{2}{19} = \frac{17}{19}$ .
[Three odd integers can be chosen in $10_{C_{3}}$ ways as there are 10 even and 10 odd integers.

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