Statistics Questions--Probability?

Question

1) Suppose that we have two events A and B with probabilities P(A)=.40 and P(B)=.60 and P(A intersect B)=.20. What is the conditional probability of P(B|A)?

2) Find the probability for P(X) U P(Xc) ?

3) We have a Venn Diagram with two events represented by sample space A and B, and these sets are: A={a,b,c,d} and B={a,a,d,d}
If we represent P(A) U P(B), we will highlight the area in the diagram where?

A) A and B share space and this area will include only a and d elements.
B) all of A and B's shared space and this area will include a, b, c, and d.
C) The area outside of A and B events and this area will include a, b, c, and d.
D) The area of A and B that is not shared and this area will include b and c.

Please explain the solving process.. Thank you.

4) We have a Venn Diagram with two events represented by sample space A and B, and these sets are: A={a,b,c,d} and B={a,a,d,d}
If we represent P(A) intersect symbol P(B), we will highlight the area in the diagram where?

A) of both circles containing a, b, c, d. B) outside both circles that do not contain a, b, c, or d.
C) where the two circles cross over that contain a and d.
D) where the two circles cross over that contain b and c.

Answer 1

1)

P(B|A) = P(A and B) / P(A) = 0.20 / 0.40 = 0.5

2)

This is not written well, it should be: P(X U Xc) = P(S) = 1 where S represents the whole sample space. This is an axiom of probability

3) answer is B as it is the union, the addition of all possible outcomes in the two events.

{a, a, b, c, d, d}

4)

the intersection is the outcomes that are in common between both sets A and B

so answer C

Answer 2

q1
0.2/0.4=0.5

q2
idk. what's Xc?

q3
B?

q4
C

Answer 3

1)P(B|A) = P(A,B)/P(A) = 0.2 / 0.4 = 0.5

2) 1

3) B {a,b,c,d}