Question

There are 4 possible routes I take to work – R1, R2, R3, and R4. The probability that I will be late due to a traffic delay when I take R1 is 0.4, R2 is 0.3, and R3 is 0.2. I take each of these routes R1, R2, R3 and R4 with probabilities 20%, 30%, 40%, and 10% respectively. If I am late to work on average 30% of the time, a) What is the probability that I will be late when I take R4? b) If I am late to work on a given day, what is the probability that I took either R2 or R3 on this day?

Answer 1

let probability of late =P(L)

a)

hence P(L)=P(R1)*P(L|R1)+P(R2)*P(L|R2)+P(R3)*P(L|R3)+P(R4)*P(L|R4)

0.3=0.2*0.4+0.3*0.3+0.4*0.2+0.1*P(L|R4)

0.1*P(L|R4)=0.05

P(L|R4)=0.5

b)

P(R3 u R4|L)= (P(R2)*P(L|R2)+P(R3)*P(L|R3))/P(L)=(0.3*0.3+0.4*0.2)/0.3=0.5667