Bayes theorem word problem

[jaymeemarissa]

So here's the problem-

At an electronics plant, it is known from past experience that the probability is 0.84 that a new worker who has attended the company's training program will meet his production quota, and that the corresponding probability is 0.45 for a new worker who has not attended the company's training program. 70% of all new workers attend the training program.

a. What is the probability that a new worker will not meet his production quota?
b. What is the probability that a new worker who does not meet his production quota will not have attended the company's training program?

I got a-
A being the worker having attended the program, B being the worker doesn't meet quota
P(B|A) = 1- .84 = .16
P(B|A')= .1- .45 = .55
P(A)= .7
P(B)= P(B|A)*P(A) + P(B|A')*P(A')
P(B)= .16*.7 + .55*.3
.277 will not meet quota

I'm stuck on b, though. Any help? Thanks!

 

[HallsofIvy]

Here's what I would do: Imagine 1000 workers. 70% of them, 700, receive the training, 300 do not. Of the 700 who receive the training, 84%, 588, make quota, 112 do not. Of the 300 who do not receive the training, 45%, 135, make quota, 165 do not. So a total of 112+ 165= 277 do not make quota, 165 of whom did not receive training.