Question

Luigi has two faulty alarm clocks that he uses to wake him up each morning. The odds that the first alarm will go off are 3:1 in favour and the odds that the second alarm will go off are 3:17 against. 1) What is the probability that both alarms go off
2) The probability to the nearest hundredth, that he is awakended by the alarm(s) is...

I got 17/20*3/4=51/80 for the first question but the second question doesn't make sense to me

Answer 1

Well given what the question says, you can't know what the probability is of him being awakened, since you don't know what's the probability of him getting awake by an alarm clock going off. But I think what they are assuming is that if a clock goes off he will awaken. So they are really asking for the probability that at least one clock goes off. Do you know how to solve for that?

Answer 2

No...

Answer 3

The answer key says 0.96 but why :/

Answer 4

Let the event the first alarm goes off be A, and let the event that the second alarm goes off be B.
P(A) = 3/4
P(B) = 17/20
\[\large P(A \cup B)=P(A)+P(B)-P(A \cap B)=\frac{3}{4}+\frac{17}{20}-\frac{51}{80}\]

Answer 5

^^ This will give you the result in the answer key for (2).