a runner is running two races. he has a 20% chance of winning race A and a 50% c

Question

a runner is running two races. he has a 20% chance of winning race A and a 50% chance of winning race B. assume the events are independent. what is the probability that he wins neither race? what is the probability that he wins one race? a runner is running two races. he has a 20% chance of winning race A and a 50% chance of winning race B. assume the events are independent. what is the probability that he wins neither race? what is the probability that he wins one race? a runner is running two races. he has a 20% chance of winning race A and a 50% chance of winning race B. assume the events are independent. what is the probability that he wins neither race? what is the probability that he wins one race? a runner is running two races. he has a 20% chance of winning race A and a 50% chance of winning race B. assume the events are independent. what is the probability that he wins neither race? what is the probability that he wins one race? a runner is running two races. he has a 20% chance of winning race A and a 50% chance of winning race B. assume the events are independent. what is the probability that he wins neither race? what is the probability that he wins one race?

Explanation / Answer

probability of winning race A = P(A) = 0.2

hence probability of loosing race A = 1-P(A) = 0.8

probability of winning race B = P(B) = 0.5

probability of loosing race B = 1-P(B)=0.5

since events are independent

P(loosing race A and loosing race B) = (1-P(A)).(1-P(B))= 0.8*0.5=0.4

P(winning one race)=P(winning race A) +P(winning raceB)-P(winning A and winning B)

                                    = 0.2+0.5-0.2*0.5

                                    =0.6

                          

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