A candidate is selected for interview for 3 posts. For the first post, there are 3 candidates, for the second, 4 and for the third post there are 2 candidates. What is the probability that the candidate is selected for at least one post?

Answer :

Probability that candidate is selected for no posts,
= (2/3)*(3/4)*(1/2)= 1/4

Probability that he selected for atleast 1 post =  1 -1/4 =3/4

probability that the candidate is selected for at least one post = 3/4

Step-by-step explanation:

Probability of selection  for 1st post  = 1/3

Probability of not selection  for 1st post  = 1 - 1/3  = 2/3

Probability of selection  for 2nd post  = 1/4

Probability of not selection  for 2nd post  = 1 - 1/4  = 3/4

Probability of selection  for 3rd post  = 1/2

Probability of not selection  for 3rd post  = 1 - 1/2  = 1/2

probability that the candidate is selected for at least one post = 1 - Probability that not selected for any post

= 1  - (2/3)(3/4)(1/2)

= 1 - 1/4

= 3/4

probability that the candidate is selected for at least one post = 3/4

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