Probability (independent?) events

Hi everyone I have a question about the following problem:

Events for a family: ${A}_{1}$ = ski, ${A}_{2}=$= does not ski, ${B}_{1}$ = has children but none in 8-16, ${B}_{2}$ = has some children in 8-16, and ${B}_{3}$ = has no children. Also, $P({A}_{1})=0.4$, $P({B}_{2})=0.35$, $P({B}_{1})=0.25$ and $P({A}_{1}\cap {B}_{1})=0.075$, $P({A}_{1}\cap {B}_{2})=0.245$. Find $P({A}_{1}\cap {B}_{1})=0.075$.

Here is my solution:

Since P(A1 and B1) = 0.075, P(A2 and B1) = 0.25-0.075= 0.175. Also since P(A1 and B2) = 0.245, P(A2 and B2) = 0.35 - 0.245 = 0.105. From this we can find P(A2 and B3) which is 0.6-0.175-0.105 = 0.32. But when I use the formula for independent events formula $P({A}_{2}\cap B3)=P({A}_{2})\ast P(B3)$ I get 0.24. Does this mean that the events are not independent? If so, how are these events not independent?

Hi everyone I have a question about the following problem:

Events for a family: ${A}_{1}$ = ski, ${A}_{2}=$= does not ski, ${B}_{1}$ = has children but none in 8-16, ${B}_{2}$ = has some children in 8-16, and ${B}_{3}$ = has no children. Also, $P({A}_{1})=0.4$, $P({B}_{2})=0.35$, $P({B}_{1})=0.25$ and $P({A}_{1}\cap {B}_{1})=0.075$, $P({A}_{1}\cap {B}_{2})=0.245$. Find $P({A}_{1}\cap {B}_{1})=0.075$.

Here is my solution:

Since P(A1 and B1) = 0.075, P(A2 and B1) = 0.25-0.075= 0.175. Also since P(A1 and B2) = 0.245, P(A2 and B2) = 0.35 - 0.245 = 0.105. From this we can find P(A2 and B3) which is 0.6-0.175-0.105 = 0.32. But when I use the formula for independent events formula $P({A}_{2}\cap B3)=P({A}_{2})\ast P(B3)$ I get 0.24. Does this mean that the events are not independent? If so, how are these events not independent?