Question

In Las Cruces the chances of bad weather that impedes driving vision is .09. On a day where the weather impedes driving vision, there is a .60 chance the traffic will be heavy and you will be late to work. If there is no bad weather, there is a .20 chance the traffic will be heavy and you will be late to work. a. Create a tree diagram and calculate all possible probabilities with (bad weather/good weather) and (late/no late) as your trees.

Answer 1

Let's define the events { bad weather} P (A)=0.09 A = P(AC) = 1-0.0g = o.gl A = { Good weather} L = { late to work} :P(LIA)=0.60 P (LI BAC) = 0.20 P (LIA) = 1-0.60=0.40 P ( Ľl Ac) =1-0.20 = 0.80 L = { no late to works Let's create tree diagram. 0.60 OPCANL) = 0.6*0.09 = 0.055 0.09 L 0.40 0.40 o PIA o P(AML)=0.40*0.09=0.036 0.20 TOP(ASO2) = 0.20*0.91=0.182 0.91 0.80 op (ACL) = 0.80*0.gg = 0.728 P(L) = P(AAL) + PLACA2) = 0.05h +0.182 P(L) = 0.236 This is the probability that you are the pearson is late to work P(2²) = 1-P (L) = 1-0.236 = 0.764