11. (NOTE: in this problem, is necessary to explain in joint notations, the prob

Question

11. (NOTE: in this problem, is necessary to explain in joint notations, the probability that is desired to determine) If you park in a certain area with yellow line, the probability that the police give you a ticket is 45%, the probability of vandalize the car is 20%. If these two events are independent, find the probability that a. Get a ticket or get the car vandalized b. Doesn't get a ticket or doesn't get the car vandalized c. Doesn't get the ticket given that the car has not been vandalize d. That the car get vandalize, given that didn't get the ticket

Explanation / Answer

A = getting a ticket
B = car gets vanadalized
P(A) = 0.45
P(B) = 0.20
A and B are independent
a)
P(A or B) = P(A) + P(B) - P(A and B)
P(A and B) = P(A) * P(B)
= 0.45*0.20 = 0.09

P(A or B) = 0.45 +0.20 - 0.09 = 0.56

b) P( A' or B') = P(A') + P(B') - P(A' and B')
= (1 - 0.45) + (1 - 0.20) - (1-0.45)(1-0.20)
= 0.91

c)
P(A' | B') = P(A' and B')/P(B') = P(A') = 1-0.45=0.55

d)
P(B|A') = P(B) = 0.20

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