Find the following probabilities after rolling a single die

Find the following probabilities after rolling a single die one time.

What is the probability of rolling a 1 on the die?

What is the probability of rolling a number less than 4?

What is the probability of rolling a number at least a 3?

What is the probability of rolling a 7 on a die?

Solution

A fair die has 1/6 probability for every number

P(1) = 1/6

P(number less than 4) = P(1,2,3) = (1/6) + (1/6 + (1/6) = 3/6 = 1/2

P(atleast 3) = P(3,4,5,6) = 4/6 = 2/3

P(7) = 0, because 7 is not on a fair die.