1. ## Probability help

Hi guys,

I have been set a few examples to work throught and ive had a go at them im just wondering if you could help me double check them as im not entirely happy.

An electronic assembly consists of two subsystems, A and B, say. After manufacture
each assembly is tested

P(A is faulty) = 0.04
P(B is faulty but A is not faulty) = 0.01
P(Both A & B are faulty) = 0.025

question1 : Calculate P(A is faulty but B is not)

my answer: 0.04 - 0.025 = 0.015

Question2 : Calculate P(B is faulty)

my answer : 0.01 + 0.025 = 0.035

Question3 : Do faults in the two subsystems occur independantly?

my answer: The two subsystems are independant as they are do not effect the other.

Question4: Calculate (A is Faulty Given That B Is Faulty)

my answer: 0.04 + 0.015 - 0.04 x 0.015 = 0.0544

So i know the last one is almost definately wrong and is there any way to mathematically determine that the two subsystems are independant of each other.

Any help is appreciated.

Cheers Guys.

2. Q1 and Q2 seem fine, drawing a venn diagram will help with events A and B being the chip is faulty.

Q3.
Two events are independent if and only if $P(A \cap B) = P(A)\cdot P(B)$
From the question we are given $P(A \cap B)=0.025$ and $P(A)=0.04$
In Q2 you calculated that $P(B)=0.035$ so that the RHS is $P(A)\cdot P(B)=0.04 \cdot 0.035=0.0014$ therefore they cannot be independent.

Q4
$P(A|B)=\frac{P(A \cap B)}{P(B)}$