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
9514 1404 393
Answer:
15.78%
Step-by-step explanation:
Let x represent the fraction of pay that Alec needs to save each week. Then at the end of 6 weeks, he will have ...
159.00 = 6(x(167.91))
x = 159.00/(6·167.91) ≈ 0.157823 ≈ 15.78%
Alec will need to save 15.78% of his pay.
_____
<em>Additional comment</em>
We recognize that $159 is almost a whole paycheck of $168, so Alec needs to save approximately 1/6 of his paycheck each week. We know that 1/6 = 16.67%, so the nearest reasonable answer choice is 15.78%.
