Problema Solution

Derek is playing a board game with three number cubes. What is the probability of Derek rolling three of a kind or a sum that is an odd number?

Answer provided by our tutors

the formula for p(a or b) is:


p(a or b) = p(a) + p(b) - p(ab)


p(a) = the probability of rolling three of a kind:


P(a) = 6/(6^3) = 1/6^2


p(b) = the probability of rolling a sum that is an odd number:


p(b) = 1/2


p(ab) is the probability of both occurring at the same time, rolling 3 of a kind whose sum is an odd number:


p(ab) = 3/6^3


p(ab) = 1/(2*(6^2))


lets plug the values into


p(a or b) = p(a) + p(b) - p(ab)


p(a or b) = 1/6^2 + 1/2 - 1/(2*(6^2))


by calculating we find:


p(a or b) = 0.5139


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the probability of Derek rolling three of a kind or a sum that is an odd number is 0.5139.