# Math Help - probability

1. ## probability

Police plan to enforce speed limits by using radar traps at different locations within the Kumasi Metropolis. The radar traps at each of the locations L1, L2, L3 and L4 are operated 40%, 30%, 20% and 30% of the time, and if a person who is speeding on his way to work has probabilities 0.2, 0.1, 0.5, and 0.2 respectively, of passing through these locations:

1. what is the probability that he will receive a speeding ticket?
\2. if a person received a speeding ticket on his way to work, what is the probability that he passed the trap located at L2

2. ## Re: probability

Originally Posted by Gad
Police plan to enforce speed limits by using radar traps at different locations within the Kumasi Metropolis. The radar traps at each of the locations L1, L2, L3 and L4 are operated 40%, 30%, 20% and 30% of the time, and if a person who is speeding on his way to work has probabilities 0.2, 0.1, 0.5, and 0.2 respectively, of passing through these locations:

1. what is the probability that he will receive a speeding ticket?
In order to get a ticket you would have to pass through location $L_1$, which has probability of .2, when the radar "trap" was operating, which has probability .4, so that both happening (passing through $L_2$ while it is operating) has probability (.2)(.4)= .08 OR pass through location $L_2$, which has probability .1, when the radar "trap" is operating, which has probability .3, so that both happening has probability (.1)(.3)= .03, or ..., etc. The total probability of all those "ors" is the sum of each probability.

2. if a person received a speeding ticket on his way to work, what is the probability that he passed the trap located at L2
I like to handle these kids of problems "en masse". That is, suppose the person drives to work 100 times. In those 100 times, he will pass $L_1$ .4(100)= 40 times and will get a ticket .2(40)= 8 times. He will pass $L_2$ .3(100)= 30 times and will get a ticket .1(30)= 3 times. He will pass $L_3$ .2(100)= 20 times and will get a ticket .5(20)= 10 times. He will pass $L_4$ .3(100)= 30 times and will get a ticket .2(30)= 6 times.

In total, then, he got 8+ 3+ 10+ 6= 27 tickets (which also gives an answer to (1)), 3 of them at $L_2$. Given that he got a ticket, the probability it was from $L_2$ is $frac{3}{27}= \frac{1}{9}$.

(Let's hope that with that many speeding tickets he loses his license and stays off the road!)