Question

Employees arrive by bus, train, or car. 20% of all employees arrive by bus, 35% by train and the rest by car. 20% of the people arriving by bus are late and 30% of the people arriving by train are late. If 25% of all employees are late,

a) Find the probability that an employee who arrives by car is late?

b) Find the probability that an employee who was late came by train?

c) Find the probability that an employee who was not late did not arrive by bus?

Answer 1

P(car) = P(bus) - P(train) = 1 - 0.20 - 0.35 = 0.45

a)

P( arrives by car is late) = P(arrive by bus are late) - P(arrive by train are late) = 1- 0.20 - 0.30 = 0.50 or 50%

P(late) = P(late by car) +P(late by bus) + P(late by train)

0.25 = 0.45*P(late and car) + 0.20*0.20+0.35*0.30

P(late and car) = 0.2333 or 23.33%

b)

P(late | train)= P(late and train)/P(late) = 0.35*0.30/0.25 = 0.42

c)

P(not late) = 1-0.25 = 0.75

P(not late did not arrive by bus) = 0.35*(1-0.30)+0.45*(1-0.23333)=0.59000 or 59%