In order to meet the criteria for promotion, an engineering company requires its
ID: 3069539 • Letter: I
Question
In order to meet the criteria for promotion, an engineering company requires its employees to pass the screening test. They are given a maximum of 3 times the chance to pass the screening test at 6-month intervals from the previous trial.
From the reports previously observed, it was found that 40% passed on the first attempt; those who did not pass at the first attempt then took the second attempt test, 60% of them successfully passed; Participants who fail on the second attempt then participate on the third attempt, 20% of them successfully passed.
So, for employees who wish to be promoted:
a. What is the probability of successfully passed at the first attempt or at the second attempt?
b. what is the probability of those who fail on the first and second attempts, then success on the third attempt?
c. What is the probability of failure in all three?
Explanation / Answer
a)P( probability of successfully passed at the first attempt or at the second attempt)
=P(passed at first attemt)+P(failed at first)*P(passed at second|failed at first)
=0.4+(1-0.4)*0.6=0.4+0.36 =0.76
b)
probability of those who fail on the first and second attempts, then success on the third attempt
=P(failed in first)*P(failed in second|failed in first)*P(passed in 3rd|failed in first 2)
=(1-0.4)*(1-0.6)*0.2=0.048
c)
P(failures in all three) =P(failed in first)*P(failed in second|failed in first)*P(failed in 3rd|failed in first 2)
=(1-0.4)*(1-0.6)*(1-0.2)=0.192