Probability Ques: Attended program?

[merci]

Hi All,
Hope there is a kind soul around to discuss with. Here goes:

1. Given that if a group of workers have attended a training program, they are able to meet the target output for 90% of the time. If new workers who do not attend, their output will be met 65%of the time. There is a group of new workers joining the company. 50% of them have attended the course. I need to find out whether the new worker has attended the training program if she has meet her output. ( No info given whether she has met target ,65% or 90% of the time)

2. I have tried using tree diagram:

New employee output time
0.5 ----> 0.9
----> 0.1
0.5 -----> 0.65
-----> 0.35

How do I do the linking of the problem above with formulas? I have just learned about conditional prob & bayes theorem.

Thanks for your views

 

[Ray Vickson]

Hi All,
Hope there is a kind soul around to discuss with. Here goes:

1. Given that if a group of workers have attended a training program, they are able to meet the target output for 90% of the time. If new workers who do not attend, their output will be met 65%of the time. There is a group of new workers joining the company. 50% of them have attended the course. I need to find out whether the new worker has attended the training program if she has meet her output. ( No info given whether she has met target ,65% or 90% of the time)

2. I have tried using tree diagram:

New employee output time
0.5 ----> 0.9
----> 0.1
0.5 -----> 0.65
-----> 0.35

How do I do the linking of the problem above with formulas? I have just learned about conditional prob & bayes theorem.

Thanks for your views

To do it systematically, first introduction some notation. Say M = {meets target}, T = {trained}. You are given the conditional probabilities P(M|T) (=?), P(M|not T) (=?) and the unconditional probability P(T) (=?). You want to know P(T|M). Do you know the formulas for getting this?

Note: I would rather not give you more help now; instead, I would like you to answer as many as you can of the questions as I asked above. Then you will be well on your way to solving the question yourself.

RGV

 

[HallsofIvy]

"( No info given whether she has met target ,65% or 90% of the time)," You are misinterpreting this information. 90% of the workers who have taken the programm meet the target, 65% of those who did not take the program meet the target. It is not a question of a percentage "of the time" for an individual.

Here's how I would do such a problem- Imagine that there are 1000 new workers (chosen to avoid decimal fractions). 50%, or 500, have attended the program, 500 have not. Of the 500 who attended the program, 90%, 450, meet the target. Of the 500 who did not, 65%, 325 meet the target. That makes a total of 450+ 325= 775 who meet the target, of whom 450 took the program.