The definition of two events being mutually exclusive (or disjoint) only means that it is not possible for the two events to occur together. Given two events, E and F, they are mutually exclusive and also mean independent.
In this case, since events E and F are mutually exclusive, therefore the probability that either E or F will occur will simply be the sum of two events.
P (E or F) = P (E) + P (F)
P (E or F) = 0.25 + 0.51
P (E or F) = 0.76
Therefore this means that there is a 76% probability that either E or F will occur.