Question

A pair of fair dice each numbered 1 to 6 is tossed . Find the probability of a score of :

i. two odd numbers.
ii. a sum of 8 or a sum of 12.
ii. both prime or both odd numbers.

Answer 1

i)

Odd numbers:

• 1, 3, 5 - 3 options of 6

P(odd and odd) = 3/6*3/6 = 1/4

ii)

Total outcomes:

• 6*6 = 36

Sum of 8:

• 2 + 6, 3 + 5, 4 +4, 5 + 3, 6 + 2 - 5 options

Sum of 12:

• 6 + 6 = 12 - 1 option

P(8 or 12) = 5/36 + 1/36 = 6/36 = 1/6

iii)

Prime numbers:

• 2, 3, 5 - 3 options of 6

Odd numbers:

• 1, 3, 5 - 3 options of 6

P(prime or odd) = 3/6*3/6 + 3/6*3/6 = 1/4 + 1/4 = 1/2