Employees at a company are rated according to their potential workload capacity

Question

Employees at a company are rated according to their potential workload capacity and the amount of formal training they have received. When the company can, it selects an employee uniformly at random to "fast-track". The proportions of its employees in each of the twelve categories appear in the following table. Let A = event that the employee chosen works at high- capacity, B = event that the chosen employee has had lots of formal training, and C = event that an employee has little or no formal training and works below high capacity. Calculate the following. (a)P(A), P(B), P(C). (b)P(A| B), P(B | B^c), P(B^c | C). (c) P(A Union B), P(A Intersection C), P(B Intersection C).

Explanation / Answer

Ans:

a)P(A)=P(High capacity)=0.1+0.15+0.16+0.22=0.63

P(B)=P(Lots of formal traning)=0.04+0.1+0.22=0.36

P(C)=P(liitle or no formal training and works below high capacity)=0.01+0.02+0.05+0.06=0.14

b)P(A/B)=P(A and B)/P(B)=0.22/0.36=0.611

P(B/Bc)=P(B and Bc)/P(Bc)=0

As,P(B and Bc)=0

c)P(A or B)=P(A)+P(B)-P(A and B)=0.63+0.36-0.22=0.77

P(A and C)=0

P(B and C)=0

None Little some lots Marginal prob. Low 0.01 0.02 0.02 0.04 0.09 Medium 0.05 0.06 0.07 0.1 0.28 High 0.1 0.15 0.16 0.22 0.63 Marginal prob. 0.16 0.23 0.25 0.36 1

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