Probability Question

Submitted by raza82 on Wed, 01/30/2013 - 15:28

 A company has told its employees that whether they receive a bonus this year will depend on whether their project is a success. which of the following probability is true?

a) P (Project Success | Receive Bonus ) does not equal P (Project Success)

b) P (Project Success AND Receive Bonus ) equals P (Receive Bonus)

c) P (Project Success OR Receive Bonus ) equals P (Project Success AND Receive Bonus)

d) P (Receive Bonus | Project Success) does not equal P (Project Success)

 

Please explain and has anyone faced such type of questions in the real exam?

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sspawar

Thu, 01/31/2013 - 01:07

 IMO

D will be the aswer

event A = bonus

event B = success

probability A is dependent of probability of B.

Suppose probability A = 0.7 and probabolity  of B = 0.9

then P(A I B) = Probability of A given B = Probability of A with probability B  will be = 0.7*0.9 = 0.63

thus 

P(A I B)  does not always equal to P ( B ). Hence only option D will be correct.

Option A is wrong, bks it is saying B is dependent of A.

Option B and C are also technically written incorrect. bks P (A and B)  means A + B, it is possible when both are independent event.

raza82

Thu, 01/31/2013 - 12:23

Explaination:

Two events A and B are independent if and only if P (A | B) = P (A) or P (B | A) = P(B) . conversely if A and B are dependent on each other , P (A|B) != P(A) and P(B|A) ! = P(B).

In other words, if two events are dependent on each other, their conditional probabilities of P(A|B) and P (B|A) will not equal their respective unconditioal probabilities. P(A), P(B).

In this example since (Receive Bonus)  is dependent on (Project Success), P (Project Success | receive Bonus) will not equal P(Project Success) . The other relationship may or may not be true.

 

This just bounces over my head, so I wonder if such type of Q's are asked in real exam? Has anyone encountered it?

sspawar

Fri, 02/01/2013 - 04:23

 I agree with you. 

on what condition option A is correct.

explanation is describing event of bonus (A) and event of success(B) are dependent on each other.

but I presume that project success (B) is not dependent of event of Bonus (A).

Here questioner if want to prove option A is correct then certainly he could not has  taken an appropriate example,

rjbuzzing

Sun, 02/03/2013 - 05:38

Can anybody comment, if these types of questions are asked in Exam ? 

sspawar

Sun, 02/03/2013 - 06:23

 certainly leave such questions.99.99% no chance. probability is 0.0001.

PROBABILITY is a vast subject, and only specialist can answer those all.

but preliminary and conceptual knowledge is must to gain.

raza82

Sun, 02/03/2013 - 07:22

That gave me a huge relief......