Question: A petroleum company intends to drill for oil in four different wells. Use the subscripts 1,2,3,4 to denote the different wells. Each well is given an equally likely chance of being successful. Consider the following events:

Event A: There are exactly two successful wells.

Event B: There are at least three successful wells.

Event C: Well number 3 is successful.

Event D: There are fewer than 3 successful wells.

Compute the following probabilities:

(a) p(A)

(b) P(B)

(c) P(c)

(e) P(AB)

(f) p(A + B)

(g) P(BC)

(h) P(B + C)

(i) P(BD)

(j) P(C)

(k) p(A|B)

(l) P(B|C)

(m) P(C|D)

(n) p(D|C)