A family has three cars, all with electric windows. Car A’s windows always work.

Question

A family has three cars, all with electric windows. Car A’s windows always work. Car B’s windows work 18.00% of the time, and Car C’s windows work 65.00% of the time. The family uses Car A 42.00% of the time; Car B 2.00% of the time; and Car C the rest of the time. You observe the family choosing their car on a certain day. Draw a tree diagram for this experiment. Firstly, the family decide which car to drive (draw three branches), then the window either works or doesn’t (two branches). Include at least 4 digits following the decimal point in your answers.

a. Compute the probability that windows will work.

b. What is the likelihood that the family will choose car B and the windows won’t work?

c. Find the probability that the family will choose car A and the windows will work or they will choose car B and the windows won’t work.

Explanation / Answer

a) probability that windows will work

=P(Car A and window works)+P(Car B and window works)+P(Car C and window works)

=0.42*1+0.02*0.18+(1-0.42-0.02)*0.65=0.7876

b)

P(family will choose car B and the windows won’t work)=P(Car B)*P(winodws not work|car B)

=0.02*(1-0.18)=0.0164

c)

P(car A and windows work+car B and window not work)

=P(car A)*P(window work|car A)+P(car B)*P(window not work|car B)

=0.42*1+0.02*(1-0.18)=0.4364

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