GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 7

Answer 1

We do not have any independence assumptions:
$$
P\left(H \mid E_1, E_2\right)=\left(P\left(E_1, E_2 \mid H\right) P(H)\right) / P(E 1, E 2)
$$
So we need to know these probabilities: $P(H), P\left(E_1, E_2 \mid H\right)$ and $P\left(E_1, E_2\right)$, which is B.

Answer 2

 

Answer 3

P(H|E1,E2)=P(H,E1,E2)/P(E1,E2)=P(H∩E1∩E2)/P(E1∩E2)=P(H∩(E1∩E2))/P(E1∩E2)={P((E1∩E2)|H)*P(H)}/P(E1∩E2)={P((E1,E2)|H)*P(H)}/{P(E1,E2)}

Now this cannot be further broken.

So D is correct option.

Answer 4

so option B is correct