help with some math problems, please?

1. Let A and B be events in a sample space S such that P(A) = 0.37, P(B) = 0.49 and P(A ∩ B) = 0.17. Find P(A | B).

a) 0.0204

b) 0.4595

c) 0.1977

d) 0.3469

e) 0.7551

f) None of the above.

2. Let A and B be events in a sample space S such that P(A) = 27⁄100 , P(B) = 49⁄100 , and P(A ∩ B) = 7⁄100 . Find P(B | Ac ).

a) 0.8571

b) 0.0959

c) 0.5753

d) 1.8148

e) 0.6712

f) None of the above.

3. Suppose that A and B are independent events. If P(A) = 7⁄10 and P(B) = 3⁄5 , find P(A ∩ B).

a) 0.06

b) 1.00

c) 0.42

d) 0.07

e) 0.13

f) None of the above.

4. Quality Control: A company has four photocopy machines A, B, C and D. The probability that a given machine will break down on a particular day is

P(A) = 13⁄100

P(B) = 9⁄50

P(C) = 1⁄5

P(D) = 13⁄100

Assuming independence, what is the probability on a particular day that all machines will break down?

a) 0.00164366

b) 0.00060840

c) 0.01000000

d) 0.00000234

e) 0.16436555

f) None of the above.