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

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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