Conditional Probabilites - What is the probability a candidate will get the job?

Question

To get a job at a government agency, a candidate needs to pass a written exam, an oral exam, and an interview. Suppose the probabilities of passing the written exam, the oral exam, and the interview are 0.8, 0.7, and 0.5 respectively. What is the probability a candidate will get the job?

Answer 1

For any 2 events A and B the joint probability that A and B both happen is given by 

 

P(A ∩ B) = P(A)*P(B|A)  

 

If A and B are independent events then P(B|A) = P(B), which means that the probability of B happening is the same regardless of whether A happens or not.  There's nothing in the statement of the problem to indicate that the 3 probabilities are not independent (and there's no information given about any potential dependence anyway) so if they are all independent then the probability that they all happen is simply the product of the individual probabilities 

 

P(get job) = 0.8*0.7*0.5 = 0.28