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 =

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.