Well, an even decimal die has probability 0.5 of rolling even and 0.5 of rolling odd.
The chances of rolling exactly one even number on five rolls is P(even)⋅(P(odd))4=0.5⋅0.54=0.55=132." role="presentation">P(even)⋅(P(odd))4=0.5⋅0.54=0.55=132.P(even)⋅(P(odd))4=0.5⋅0.54=0.55=132.
The chances of rolling exactly three even numbers on five rolls is (P(even))3⋅(P(odd))2=0.53⋅0.52=0.55=132" role="presentation">(P(even))3⋅(P(odd))2=0.53⋅0.52=0.55=132(P(even))3⋅(P(odd))2=0.53⋅0.52=0.55=132.
The chances of rolling exactly five even numbers on five rolls is (P(even))5=0.55=132" role="presentation">(P(even))5=0.55=132(P(even))5=0.55=132.
Further, the probability of independent events is the sum of their probabilities, so the probability of rolling an odd number of even numbers is 332" role="presentation">332