Question

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

विकल्प

•  \[\frac{2}{19}\]

•  \[\frac{3}{29}\]

• \[\frac{17}{19}\]

• \[\frac{4}{19}\]

Answer 1

\[\frac{17}{19}\]
\[P\left( \text{ product is even } \right) = 1 - P\left( \text{ product is odd } \right)\]
\[\text{ For the product to be odd, the two digits must be odd } .\]
\[\text{ Now, 10 numbers are odd in the first 20 integers . } \]
\[ \therefore P\left( \text{ product is even} \right) = 1 - \frac{10}{20} \times \frac{9}{19} \times \frac{8}{18}\]
\[ = 1 - \frac{9}{38} \times \frac{8}{18}\]
\[ = 1 - \frac{2}{19}\]
\[ = \frac{17}{19}\]