Cap'n, you're much more learned than me so correct me if I am wrong, but doesn't P(E union F) mean P(E or F), not P(E and F)?.

Since E and F are independent, P(E)P(F)=(.35)(.45)=.1575

P(E or F)=P(E)+P(F)-P(E or F)=.35+.45-.1575=.6425, assuming they're not mutually exclusive.

Then again, mutually exclusive events can not be independent events.