GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 4

Answer 1

P(A,B) = P(A) P(B,A)

since  P(A,B) decreases with increase in P(A)

therefore P(A) is inversely proportional to P(A,B)

which implies that P(A,B) is directly proportional to P( B | A )

Comments

why not A option correct ?  According to this statement  P(A,B) is directly proportional to P( B | A )  true

but  P(A|B) is also  proportional to P(A, B)   so it will also decrease . ??

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Notice that as it was mentioned “P(A,B) decreases while P(A) increases”. Now using equation P(A,B) = P(A) P(B|A) it was able to conclude that  P(A) is inversely proportional to P(A,B) and P(B|A) directly proportional to P(A,B) and so P(B|A) decreases

In eqaution P(A,B) = P(B) P(A|B), the only known thing is P(A,B) decreases and nothing else. So we cannot tell anything about P(A|B)

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A.P(A/B)=P(A,B)/P(B) ,P(A,B) decreases but we don't know P(B) is decreases or increases so we can’t say anything about P(A/B) decreases or not

B.P(B/A)=P(A,B)/P(A) as P(A,B) decreases and P(A) increases so P(B/A) is definitely decreases as P(A) is inversely proportional to P(B/A)

Answer 2

A and B are the two events .P(A,B)=P(B|A)*P(A) => P(B|A)=P(A,B)/P(A)  If P(A,B) decreases and P(A) increases then  automatically P(B|A) decreases.