Three integers are chosen at random from the first 20 integers. T… - Vidyadip

Question

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

$\frac{2}{19}$
$\frac{3}{29}$
$\frac{17}{19}$
$\frac{4}{19}$

✓

Answer

$\frac{17}{19}$

Soluction:
Required probability that product of two integers should be even.
10 integers are odd out of first 20 integers.
Required probability = 1 - Probability of product is odd
Product of three integers is odd if two numbers are odd
Required probability $=1-\frac{10}{20}\times\frac{9}{19}\times\frac{8}{18}=\frac{17}{19}$

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