1. Some questions on probability

Hello, I have a few questions:
The 160 pupils at a certain village school are all registered with the school dentist. Of the 75 girls only 25 of them have seen the dentist in the past year for treatment, the others have not. However, 34 of the boys have received treatment and the rest have not. Each child's records are kept on a separate record card.
A record card is selected at random. Let A represent the event that the child referred to on the card has received treatment in the past year, and the event BN represent that the child referred to is a boy. Find P(A intersect B)

I found that P(B)=1732. Also, the answer to this question is 17/80.

I'm also confused as to what you'd for the next part of the question, which is
Find P(A' intersect B')

The other question I'm stuck on is this:
In a factory, machinese A, B and C produce electronic components. Machine A produces 16% of the components, machine B produces 50% of the components and machine C produces the rest. Some of the components are defective. Machine A produces 4%, machine B 3% and machien C 7% defective components.
Draw a tree diagram to represent this information.

I would really appreciate any help, thanks!

2. Hello, sakuraxkisu!

The 160 pupils at a certain village school are all registered with the school dentist.
Of the 75 girls, only 25 of them have seen the dentist in the past year, the others have not.
However, 34 of the boys have seen the dentist, and the rest have not.
Each child's records are kept on a separate record card.

A record card is selected at random.
Let A represent the event that the child on the card has seen the dentist in the past year.
Let B represent that the child referred to is a boy.

(a) Find P(A intersect B)

We have the following facts:

. . $\text{75 girls} \quad\Rightarrow\quad \begin{Bmatrix}25 & \text{dentist} \\ 50 & \text{not-d} \end{Bmatrix}$

. . $\text{85 boys} \quad\Rightarrow\quad \begin{Bmatrix}34 & \text{dentist} \\ 51 & \text{not-d} \end{Bmatrix}$

$P(A \cap B) \;=\;P(\text{dentist} \cap \text{boy}) \;=\;\dfrac{34}{160} \;=\;\dfrac{17}{80}$

(b) Find P(A' intersect B')

$P(A' \cap B') \;=\;P(\text{not-d} \cap \text{girl}) \;=\;\dfrac{50}{160} \;=\;\dfrac{5}{16}$

3. The answer that I've been to given to (b) was 63/80, so you've gone wrong somewhere. But thank you for helping me with the (a)