Some years ago, Dr. Wolff had two young sons (Tim and Dave) and two lawn mowers

ID: 3352867 • Letter: S

Question

Some years ago, Dr. Wolff had two young sons (Tim

and Dave) and two lawn mowers

(yellow and green). The probability of Tim being re

ady and willing to mow is 0.40, and for

Dave, 0.20. The probability the mowers will start i

s Pr (green) = 0.90 and

Pr (yellow) = 0.80.

a. Assuming that all events are independent, what i

s the probability of getting the lawn

mowed with no problem? Hint: draw a separate Venn d

iagram for sons and for lawn

mowers, and then combine.

b. What is the probability of getting both sons and

both mowers working at the same time?

c. Construct a joint probability table of all indep

endent outcomes, with sons = 0,1,2 across

the top and mowers = 0,1,2 along the left side.

d. From the table, find the probability of having t

wo sons available, but only one mower.

P ( someone is willing to mow) = 0.4+0.2-0.4*0.2=0.52

P( one of the mowers will start) = 1-(0.1)*(0.2) = 0.98

P( lawn will get mowed) = 0.52*0.98=0.5096

b) P( both sons and both mowrs) = 0.4*0.2*0.8*0.9= 0.0576

d) P( both sons and one mower ) is 0.3168

Sons 0 1 2 Total Mower 0 0.0096 0.0088 0.0016 0.02 1 0.1248 0.1144 0.0208 0.26 2 0.3456 0.3168 0.0576 0.72 Total 0.48 0.44 0.08 1

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.