Question

(A) Police plan to enforce speed limits by using radar trapsat 4 different locations within the city limits. The radar traps ateach 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 hisway to work has probabilities of 0.2, 0.1, 0.5, and 0.2,respectively, of passing through these locations, what is theprobability that he will receive a speeding ticket?

(B) The person received a speeding ticket on his way towork, so what is the probability that he passed through the radartrap located at L2?

Answer 1

0.27

0.1111111

Explanation:

Given that:

X :

L1 = 40% = 0.4

L2 = 30% = 0.3

L3 = 20% = 0.2

L4 = 30% = 0.3

P(x) :

L1 = 0.2

L2 = 0.1

L3 = 0.5

L4 = 0.2

A.)

Σ(X * p(x))

(0.4 * 0.2) + (0.3*0.1) + (0.2*0.5) + (0.3 * 0.2) = 0.27

B.) Radartrap located at L2:

P(L2) = (L(x2) * p(L2)) / Σ(X * p(x))

= (0.1 * 0.3) / 0.27

= 0.1111111