Question

Dungeon and Dragons (old popular boardgame) uses a twenty-sided number cube (die), what is the probability that you will roll an even or an odd prime number? The number 1 isn’t an odd prime. Round to three decimals.

Answer 1

P(even or odd prime) = 0.85

There is 85% probability of rolling an even number or odd prime number.

Explanation:

We are given a twenty-sided die which means it has faces from 1 to 20, so that means the total number of outcomes are 20.

We are asked to find the probability of rolling an even number or odd prime number.

We know that probability is given by

P = Number of desired outcomes/Total number of outcomes

Let us first count the number of desired outcomes.

In the range of 1 to 20 we have following even numbers,

2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (10 outcomes)

P(even) = 10/20

P(even) = 0.50

In the range of 1 to 20 we have following odd prime numbers,

3, 5, 7, 11, 13, 17, 19 (7 outcomes)

P(odd prime) = 7/20

P(odd prime) = 0.35

So the required probability is

P(even or odd prime) = 10/20 + 7/20

P(even or odd prime) = 0.50 + 0.35

P(even or odd prime) = 0.85

Therefore, there is 85% probability of rolling an even number or odd prime number.

Note: Since we are asked to find the probability of rolling an even number or odd prime number, that's why we have added the probabilities of these two events.

OR corresponds to addition of probabilities

AND corresponds to multiplication of probabilities