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If the probability of a event is zero, then the event cannot occur. Therefore, if the probability of an even number is zero, then the probability of an odd number is one.
If you have an equal amount of odd and even numbers in a determined sample space, the probability of choosing and odd number is 1/2 (.5).
50 50 odd or even same probability
The probability that, when rolling three dice none will come up odd is broken down by the probability that on odd roll will occur as an independent event. Rolling the first die has a probability of 3/6 that it will be odd. Rolling the second has the probability of 3/6 that it will be odd. Rolling the third has a probability of 3/6 will be odd. Rolling three and coming up with odd is really the probability that no odd numbers occurred, so therefore an even number DID happen (3/6), and an even number DID happen (3/6), and an even number DID happen (3/6). That's really just 1 - (3/6^3) or simplified 1 - (1/2^3). So therefore the probability that an odd number occurred in 3 die rolls is about 87.5%.
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