Three distinct integers are chosen at random from the first 20 positive integers. Compute the probability that: (a) their sum is even; (b) their product is even.

Step-by-step explanation:

There are first 20 positive integers 1,2...20. Three distinct integers are chosen at random.

Total no of ways of drawing 3 integers =

To  Compute the probability that: (a) their sum is even

a) Sum can be even if either all 3 are even or 1 is even and 2 are odd.

There are in total 10 odd and 10 even.

Ways of sum even =

Prob =

b) their product is even

Here any one should be even or both

SO no of ways are

=

Prob =

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.