Probability answers check :)

[Dumpling]

Hi everyone, I was hoping someone out there who has done probability before can help me out with some questions

Probability is what I find hardest of all these topics covered so I'm just starting early ><

Question 1:

If P(A)=0.4, P(B)=0.5 and P(A or B')=0.1 -> Note: B' is B not occurring ~~

Find
(a). P(A and B)
(b). P(A or B)
(c). P(A' or B')
(d). P(A' or B)
(e). P(B|A)

My answers for question 1 were:
(a). 0.2
(b). 0.7
(c). 0.3
(d). 0.8
(e). 0.5


Question 2:

Let P(A)=0.3 and P(B)=0.6

(a). Find the probability of A or B when A and B are independent.
(b). Find P(A|B) when A and B are mutually exclusive.
(c). Find P(A|B') when A and B are mutually exclusive.

My answers for question 2 were;
(a). 0.72
(b). cannot exist (?)
(c). 0.5

THE FOLLOWING QUESTIONS ARE THE ONES I TIRED BUT I DONT REALLY UNDERSTAND WHAT TO DO WHY IS PROBABILITY SO HARD TO UNDERSTAND

Question 3

Let A and be events with probabilites P(A)=3/4 and P(B)=1/3. Show that 1/12 equal to/less than sign P(A and B) equal to/less than 1/3. (Hint: draw Venn diagrams for all possible relations for A and B). NOTE: sorry if this question is confusing since Im new here and I dont know how to use the maths symbols yet )

Question 4

Let A and B be two events such that P((A or B))' = 0.6 and P(A and B)=0.1. Let C be the event that either A or B but not both will occur. Compute P(C|A or B).

If anyone can check answers with me or help out with some questions that would be great Thank you for the help in advance and yes I think I will be getting off now.. its so late and still doing maths

If anyone knows any good books with a lot of probability questions please recommend me

Sorry in advance if this post is really messy and sloppy as I am new here .. and just a student that needs help ..
Will leave how to input maths symbols tomorrow >

[Dumpling]

Sigh I cant sleep either because I am also working on another two questions which are so hard too.. Wonder why these questions are so hard with no solutions or working out?

If possible can someone guide me in doing these two questions as well please? Thank you ~~

Question 5

Jane has three children, each of which is equally likely to be a boy or a girl independently of the others. Define the events

A = { all the children are of the same sex } ,
B = { there is at most one boy },
C = { the family includes a boy and a girl }

(a). Show that A is independent of B, and that B is independent of C.
(b). Is A independent of C?
(c). Do the results in (a) hold if Jane has four children? Explain.

Question 6

A toy manufacturer buys ball bearings from three different suppliers - 50% of her total order comes from supplier 1, 30% from supplier 2 and the rest from supplier 3. Past experiences has shown that the quality control standards of the three suppliers are not all the same. Two percent of the ball bearings produced by supplier 1 are defective, while suppliers 2 and 3 produce defective bearings 3% and 4% of the time, respectively. What is the proportion of the ball bearing in the toy manufacturer's inventory are defective?

Thank you ~~

[Kiro Kompiro]

I'm just getting this myself so here goes.

First things first

"And" is represented by the UPSIDE DOWN "U". This means: "what is the chance of BOTH events happening: BOTH conditions must be true".   

"OR" is represented by the normal "U".  This means what is the chance of either being true.

This can sound counter-intuitive, as A U B in set notation means A union B, suggesting "AND", but its not. 

In fact Pr(A U B) reads "the probability of A OR B".

try this: http://www.regentsprep.org/regents/math/ALGEBRA/APR8/LProbAO.htm

My teacher was confusing this as well, and after a lengthy debate and going over th text books, she agreed.

With that of the way, I'm nor sure if the "and" in your question means U or "upside down" U?

[Kiro Kompiro]

Q1
 a) 0.1 assuming A and B are independent events
b) 0.7
c) 0.8
d) 0.3
e) 0.5

q2
a)0.72
b) 0 ( which means cannot exist, so this is a trick question, need to know that a certain event has Pr=1 and an event that never will happen has Pr=0
c) 0.75