Question

a)   A company has taken a ballot of its workforce, asking them to choose between two alternative new schemes (A and B) for claiming travelling expenses. 60% of the workforce support scheme A, while 50% of these owning a car. If only 30% of those who support scheme B own a car, calculate the probability that if a worker is chosen at random, he will be:

    i.       a car owner

  ii.       a car owning, scheme A supporter

 iii.       a car owner, given that he supports scheme A

 iv.       a scheme A supporter, given that he owns a car

Answer 1

Probability of workforce who support scheme A $P(A)=0.6$

Probability of workers who support scheme B $P(B)=0.4$

Let X denote that person owns a car-

Probability that person support A scheme and owns a car $P(\dfrac{A}{X})=0.5\times 0.6=0.30$

Probability that person support B scheme and owns a car $P(\dfrac{B}{X})=0.3\times 0.4=0.12$

(a) Probability that a worker is car owner $P(X)=P(\dfrac{A}{X})+P\dfrac{B}{X})=0.30+0.12=0.42$

(b) Probability that worker owns a car and support A schme $P(\dfrac{A}{X})=0.30$

(c) Probability that worker is a car owner, given that he supports scheme A

$=\dfrac{P(X)}{P(A)}=\dfrac{0.42}{0.6}=0.7$

(d) Probability that woker is schemeA , suppoter given that he owns a car$=\dfrac{P(A)}{P(X)}={0.6}{0.42}=0.3$