Question

An event is three times as likely as its complement. What is the probability of the event?

Answer 1

E = some event
C = complement of event E
Since the events are complementary, this means P(E)+P(C) = 1

We know that P(E) = 3*P(C) since "an event is three times as likely as its complement"

So we can replace P(E) with 3*P(C) and then isolate P(C)
P(E) + P(C) = 1
3*P(C) + P(C) = 1
4*P(C) = 1
P(C) = 1/4

The probability of the complementary event is 1/4
So the probability of the original event is 3/4 (three times 1/4)

Answer: 3/4

note: in decimal form, 3/4 = 0.75