Question

A training program is used by a corporation to direct hirees to appropriate jobs. The program consists of two steps. Step I identifies 33​% as management​ trainees, 62​% as nonmanagerial​ workers, and 5​% to be fired. In step​ II, 71​% of the management trainees are assigned to managerial​ positions, 24​% are assigned to nonmanagerial​ positions, and 5​% are fired. In step​ II, 60​% of the nonmanagerial workers are kept in the same​ category, 12​% are assigned to management​ positions, and 28​% are fired. What is the probability that a randomly chosen hiree will be fired at the end of the training​ period?

Answer 1

This question is solved using the tree diagram which is given below.

P(Fired) = P(Fired in step I) + P(management trainee in step I and fired in step II) + P(nonmanagerial worker in step I and fired in step II)

              = 0.05 + (0.33 * 0.05) + (0.62 * 0.28)

              = 0.2401

Therefore, the probability that a randomly chosen hiree will be fired at the end of the training period is 0.2401