If a 20-sided fair die with sides distinctly numbered 1 through 20 is rolled, the probability that the answer is a perfect square can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

the only squares from 1 to 20 are

1 , 4, 9, 16, that would be 4 of them
So the prob(square) = 4/20 = 1/5

if 1/5 = a/b , in lowest terms, then
a+b = 1+5 = 6

4 perfect squares out of 20 possibilities

4/20 = 1/5, so 1+5 = 6

A fair icosahedral die(number 1-20) is rolled. What is the probability that it will show: a factor of 20 or a prime number?

To find the probability that the answer is a perfect square when a 20-sided die is rolled, we need to determine how many of the outcomes are perfect squares and divide that number by the total number of possible outcomes.

A perfect square is a number that can be expressed as the square of an integer. In this case, the perfect square outcomes would be 1, 4, 9, and 16 because these numbers have integer square roots.

Now, let's count the total number of possible outcomes. Since we are rolling a 20-sided die, there are 20 possible outcomes, numbered from 1 to 20.

Out of these 20 possible outcomes, there are 4 perfect squares.

Therefore, the probability that the answer is a perfect square is 4/20 = 1/5.

To express this probability as a fraction with coprime positive integers, we can simplify 1/5 as follows:

1/5 = (1 × 1)/(1 × 5) = 1/5.

Therefore, a = 1 and b = 5.

So, a + b = 1 + 5 = 6.

The value of a+b is 6.