GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 9

Answer 1

A counter example: if we have two events $A, B$ such that $P(B)>0$ and $P(A)>0$, but $A \cap B=\emptyset$, then $P(A \mid B)=0,$ but $P(A)>P(A \mid B)$. It's easy to come up with examples like this: for example, take any sample space with event $A$ such that $P(A)>0,$ and $P\left(A^c>0\right)$, it follows that $P\left(A \mid A^c\right)=0,$ but $P(A)>0.$

Answer 2

.

Comments

shouldn’t P(B) be 4/8, though it will reduce to same value but if we count the elements out of total then..

---

yep.

---

How option C is correct?

---

Rearrange the terms 

Bring the 1 from RHS to LHS.Now even if P(A ∩ B) is 0,the LHS would be still greater than equal to P(A)+P(B), no matter what the probabilities of both the events might be.