We need to set up a system, rather than a single equation, because there are two variables involved.
The first equation represents the fact that the two numbers are in a 3:2 ratio:
The second equation represents the fact that their sum is 35:
So, we have the following system:
Using the expression for x in the first equation, the second one becomes
which implies
Multiplying both sides of the equation by 3 and substituting 4 for p
Answer:
C) 0.880
B) 0.075
Step-by-step explanation:
If the professor forgets to set the alarm
Probability = 0.1,
Wakes up in time probability = 0.25.
If the professor sets the alarm
Probability = 1 - 0.1 = 0.9
Wake up in time probability = 0.95.
A.)
The probability that professor Moore wakes up in time to make his first class tomorrow
Probability = ( Forgets to set alarm probability x Wakes up in time )+ ( Sets the alarm probability x Wakes up in time ) = ( 0.1 x 0.25 ) + ( 0.9 + 0.95 ) = 0.88
B.)
Late in the class
Set the Alarm Probability = 0.1
Wakes up late probability = 1 - 0.25 = 0.75
Professor Sets the alarm probability = Set the Alarm Probability x Wakes up late probability = 0.1 x 0.75 = 0.075
