John and Bob both go to a party which starts at 5:00. Each of them arrives at a random time between 5:00 and 6:00. What is the probability that the number of minutes Grogg is late for the party plus the number of minutes Winnie is late for the party is less than 45? Express your answer as a common fraction.

wiskdls
Apr 15, 2018

#1**+1 **

It seems that "John" and "Bob" have somehow morphed into "Grogg" and "Winnie"...

But, anyway.....call the number of minutes that one of tthem could be late = x

And call the number of minutes that the other could be late = y

So......the total possible minutes that they could be late is 60 minutes each...so...we have this equation of a line

x + y ≤ 120 (1)

But....we are looking for this x + y ≤ 45 (2)

Look at the graph here : https://www.desmos.com/calculator/90isasjiab

The area of the triangle formed by (1) in the first quadrant is (1/2)base * height =

(1`/ 2) (120) (120) = 14400 / 2 = 7200 units^2

The area of (2) in the first quadrant is (1/2)(45) (45) = 1012.5 units^2

So....the probability that the sum of the minutes that both are late is ≤ 55 is

1012.5 / 7200 = 9 / 64

CPhill
Apr 15, 2018