A single fair die is rolled. Find the probability of each of the following events, and write your answers as fractions.

Question

A single fair die is rolled. 

Find the probability of each of the following events, and write your answers as fractions.  

 

a) The number showing is 2:      P(2) = 

b) The number showing is not 2:   P(not 2) = 

c) The number showing is even.   P(even) = 

 

d) The number showing is greater than 4.   P(greater than 4 ) = 

 

e) The number showing is 2 or even.     P(2 or even) =

Answer 1

Assuming your "fair die" is 6-sided number 1 to 6:

a) The number showing is 2: P(2) = 1/6

b) The number showing is not 2: P(not 2) = 1 - 1/6 = 5/6

c) The number showing is even. Evens are 2, 4, 6 so P(even) = 3/6 = 1/2

d) The number showing is greater than 4. Greater then 4 = 5. 6 so P(greater than 4 ) = 2/6 = 1/3

e) The number showing is 2 or even. Since 2 cannot be counted twice (once as a 2 and once as an even), P(2 or even) = 3/6 = 1/2. Mathematically this is calculated P(A or B) = P(A) + P(B) - P(A and B) = P(2) + P(even) - P(2 and that the result is even) - 1/6 + 3/6 - 1/6 = 3/6 = 1/2