Question

You roll a six- sided die. Find the probability of each of the following scenarios
a. Rolling a 6 or a number greater than 3
b. Rolling a number less than 5 or an even number
c. Rolling a 2 or an odd number

Answer 1

Part a

P(Rolling a 6 or a number greater than 3) =P(Rolling a 6) + P(Number greater than 3) – P(Rolling a 6 and number greater than 3)

P(Rolling a 6) = 1/6

P(Number greater than 3) = 3/6

P(Rolling a 6 and number greater than 3) = 1/6

P(Rolling a 6 or a number greater than 3) = (1/6) + (3/6) – (1/6) = 3/6 = ½ = 0.50

Required probability = 0.5000

Part b

P(Rolling a number less than 5 or an even number) = P(Rolling a number less than 5) + P(an even number) – P(Rolling a number less than 5 and an even number)

We have

Rolling a number less than 5 = 1,2,3,4

An even number = 2,4,6

P(Rolling a number less than 5) = 4/6

P(an even number) = 3/6

P(Rolling a number less than 5 and an even number) = 2/6

P(Rolling a number less than 5 or an even number) = (4/6) + (3/6) – (2/6) = (4 + 3 – 2) / 6 = 5/6 = 0.833333333

Required probability = 0.833333333

Part c

P(Rolling a 2 or an odd number) = P(Rolling a 2) + P(odd number) – P(rolling a 2 and odd number)

P(Rolling a 2) = 1/6

P(odd number) = 3/6

P(Rolling a 2 and odd number) = 0

(Rolling a 2 and rolling an odd number are independent events.)

P(Rolling a 2 or an odd number) = (1/6) + (3/6) + 0 = 4/6 = 0.666666667

Required probability = 0.666666667