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  • A company employs two types of workers: Type A and Type B. Type A workers make up 60% of the workforce and Type B workers make up the remaining 40%. Type A workers produce 80% of the tota

A company employs two types of workers: Type A and Type B. Type A workers make up 60% of the workforce and Type B workers make up the remaining 40%. Type A workers produce 80% of the total output, while Type B workers produce only 20% of the total output. If a worker is selected at random and is found to have produced a certain output, what is the probability that the worker is of Type B? 

Option: 1

0.1345


Option: 2

0.1234


Option: 3

0.1483


Option: 4

0.1429


Answers (1)

best_answer

Let A be the event that a worker is of Type A, and B be the event that a worker is of Type B. Let O be the event that a worker produces a certain output. 

We want to find the probability of event B given O, i.e., P(B|O). 

Using Bayes' theorem, we have:

P(B / O)=\frac{P(O / B) \times P(B)}{P(O)}

We know that,

P(B) = 0.4 (since Type B workers make up 40% of the workforce)

P(A) = 0.6 (since Type A workers make up the remaining 60%)

We also know that Type A workers produce 80% of the total output, and Type B workers produce 20% of the total output. 

So, the probability of producing a certain output given that the worker is of Type A is 0.8, and the probability of producing a certain output given that the worker is of Type B is 0.2. Therefore, 

P(O|A) = 0.8 and P(O|B) = 0.2 

To find P(O), we can use the law of total probability:

P(O)=P(O / A) \times P(A)+P(O / B) \times P(B)

\begin{aligned} & \Rightarrow P(O)=0.8 \times 0.6+0.2 \times 0.4 \\ \\& \Rightarrow P(O)=0.56 \end{aligned}

Substituting all these values into Bayes' theorem, we get:

\begin{aligned} & P(B / O)=\frac{0.2 \times 0.4}{0.56} \\ \\& \Rightarrow P(B / O)=0.1429 \end{aligned}

Therefore, the probability that a worker who produced the certain output is of Type B is approximately 0.1429.

Posted by

seema garhwal

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