Question

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What is the probability of rolling at most one even number with two standard six-sided dice? We can assume both dice are fair.

Answer 1

Given that there are two six faced die. When we, roll then together, the sample space is

S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Total number of outcomes is 36.

Now, at most one even number means, either 0 even number or 1 even number. The outcomes favoravle to this event are {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,3),(2,5),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,3),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,3),(6,5)}

Favorable number of outcomes is 27

Therefore, Required probability, P(rolling at most one even number with two fair dice)