# Could I have some help solving this conditional probability problem?

The probability of event $A$ occurring is $P(A)=13/25$.The probability of event B acquiring is $P(B) = 9/25$. The conditional probability of $A$ occurring given that $B$ has occurred is $P(A|B) = 5/9$

(a) Determine the following probabilities

i - $P( A$ and $B)$

ii - $P(B|A)$

iii- $P(A$ or $B$ or both)

iv- P(Not A | Not B)

(b) Determine $P( A$ occurs or $B$ does not occur), show your working

I have done the first $3$ parts of the question $18$ (a(i-iii)) but at fourth part of a and part $b$, I wasn't sure how to work it out

ai- $1/5$

aii- $5/13$

aiii- $17/25$

aiv- $1/2$

b-$21/25$

This is an a level question and any help will be much appreciated.

$$P(A^c \mid B^c) = \frac{ P(A^c \cap B^c) }{P(B^c)} = \frac{P( (A \cup B)^c )}{P (B^c)}$$
Hint for b): $$P(A \cup B^c) = P(A) + P(B^c) - P(A \cap B^c)$$ For that last intersection you can apply the rule that $$P(A \cap B) = P(A \mid B)P(B)$$ and then look back at a) iv