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Answer:
The probability of a selected car being a 4 door car, given that the car has a sunroof = 0.40
Step-by-step explanation:
The complete question is presented in the attached image.
The conditional probability, of event A happening, given that event B has happened, P(A|B), is given mathematically as
P(A|B) = P(A n B) ÷ P(B)
So, the required probability of a selected car being a 4 door car, given that the car has a sunroof is given as
P (4 doors | sunroof)
= P (4 doors n sunroof) ÷ P(sunroof)
Note that the probability of an event is given as the number of elements in that event divided by the Total number of events.
P (4 doors n sunroof)
= n (4 doors n sunroof) ÷ n (total)
From the Venn Diagram in the attached image,
n (4 doors n sunroof) = 20 + 0 = 20
n (total) = 100
P (4 doors n sunroof) = (20/100) = 0.20
P(sunroof) = n(sunroof) ÷ n(total)
n(sunroof) = 12 + 18 + 20 + 0 = 50
n(total) = 100
P(sunroof) = (50/100) = 0.50
P (4 doors | sunroof)
= P (4 doors n sunroof) ÷ P(sunroof)
= (0.20/0.50) = 0.40
Hope this Helps!!!
