Question

J and K are independent events. P(J | K) = 0.1. Find P(J)

Answer 1

$\mathbb P(J|K)=\dfrac{\mathbb P(J\cap K)}{\mathbb P(K)}=\dfrac{\mathbb P(J)\mathbb P(K)}{\mathbb P(K)}=\mathbb P(J)$

because $\mathbb P(J\cap K)=\mathbb P(J)\mathbb P(K)$ due to independence. So $\mathbb P(J)=0.1$.