An insurance company studies back injury claims from a manufacturing company. The insurance company finds that 40% of workers do no lifting on the job, 50% do moderate lifting and 10% do heavy lifting. During a given year, the probability of filing a claim is 0.05 for a worker who does no lifting, 0.08 for a worker who does moderate lifting and 0.20 for a worker who does heavy lifting. A worker is chosen randomly from among those who have filed a back injury claim. Calculate the probability that the worker’s job involves moderate or heavy lifting.

0.75

Explanation:

P(no lifting) = 0.4

P(moderate lifting) = 0.5

p(heavy lifting) = 0.2

P(Claim | no lifting) = 0.05

P(Claim | moderate lifting) = 0.08

P(Claim | heavy lifting) = 0.2

Using BAYE Theorem

P(no lifting claim) = P(Claim | no lifting)*P(no lift) / P(Claim)

P(Claim) = (Claim | no lifting)*P(no lifting) + P(Claim | moderate lifting)*P(moderate lifting) + P(Claim | heavy lifting)*p(heavy lifting)

P(Claim) = (0.05)*(0.4) + (0.08)*(0.5) + (0.2)*(0.1)

P(Claim) = 0.08

P(no lifting claim) = (0.05)*(0.4) / 0.08

P(no lifting claim) = 0.25

P(Heavy or moderate lifting | Claim) = 1 - 0.25

P(Heavy or moderate lifting | Claim) = 0.75