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praet you asked for some good problems in probability, statistics...

Two events A & B are independent. If P(A) = 0.83, P(B) = 0.25. If C is a set of possible values of probability that A & B both occur, Find the range of C?

If the events are independent .. P(A/B) = P(A) similarly ...P(B/A) = P(B)

P(A and B) = P(A ) * P (B) = 0.83 * 0.25 = 0.83/4

Is there a range for the values of C...there is just one probability...

Folks there was a type with the question. Kindly read as:
Two events A & B are such that P(A) = 0.83, P(B) = 0.25. If C is a set of possible values of probability that A & B both occur, Find the range of C?

Folks there was a type with the question. Kindly read as: Two events A & B are such that P(A) = 0.83, P(B) = 0.25. If C is a set of possible values of probability that A & B both occur, Find the range of C?

Ok so we dont know if the events are independent or not.

P(A/B) = P(A and B) / P(B)

C = P(A/B) * P(B)

We have two cases

1. Both events can be mutually exclusive...as in... heads on a coin and a six on a die..

P(A/B) = 1

2. Both events can be independent , in that case ...

P(A/B) = P(B) ..In case , the required probability is 0.83/4

3. Both events cannot occur together ..as in.. heads and tails in the same toss.

Folks there was a type with the question. Kindly read as: Two events A & B are such that P(A) = 0.83, P(B) = 0.25. If C is a set of possible values of probability that A & B both occur, Find the range of C?

Ok so we dont know if the events are independent or not.

P(A/B) = P(A and B) / P(B)

C = P(A/B) * P(B)

We have two cases

1. Both events can be mutually exclusive...as in... heads on a coin and a six on a die..

P(A/B) = 1

2. Both events can be independent , in that case ...

P(A/B) = P(B) ..In case , the required probability is 0.83/4

3. Both events cannot occur together ..as in.. heads and tails in the same toss.

P(A/B) = 0

Range : Max - Min = 1 - 0 = 1 ?

thanks praetorian

there should be no difference between 1 and 3. Mutually exclusive events are, by definition, events that cannot happen at the same time.
_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

very good.. u are on target..but missed it slightly.
First, a silly mistake in calculation
P(A or B or both) = 1.08 - P(A & B)
It is correct that Minimum of P(A&B) = .08

praet why do u say that max of P(A & B) occurs when events are independent? Independent events just mean that probaility of one does not affect that of other i.e. outcome of second event is idependent of outcome of first and vice-versa.

Okay, Now how do u find the maximum?
Can u use set theory. Just draw two vien diagram of A & B, knowing that they intersect. Can u find out for what set A & B intersection will be Max.
thanks.

very good.. u are on target..but missed it slightly. First, a silly mistake in calculation P(A or B or both) = 1.08 - P(A & B) It is correct that Minimum of P(A&B) = .08

praet why do u say that max of P(A & B) occurs when events are independent? Independent events just mean that probaility of one does not affect that of other i.e. outcome of second event is idependent of outcome of first and vice-versa.

Okay, Now how do u find the maximum? Can u use set theory. Just draw two vien diagram of A & B, knowing that they intersect. Can u find out for what set A & B intersection will be Max. thanks.

Thanks...minimum is 0.08.
yeah, i was totally wrong.

Maximum will occur when B is a subset of A.
In that case , C =0.25
Maximum C = 0.25

There u go... good. a simple but conceptual question.
i invented this question after reading prob. notes of OG.
will see if i can come up with more.
thanks