Question

There are 18,000 adults who belong to a nationwide chess club. Among the 18,000 adults, 8,000
prefer to play with white(W), whereas the rest prefer black(B). Among all members, 11,000 prefer
to play chess on the computer(C), the others prefer the regular board(RB). 3,000 members prefer
to play with white on the computer. Suppose an adult club member is selected at random.
(a) Find the probability that the person prefers to play with black. That is, find P(B).
(b) Find the probability that the person prefers to play with black on the regular board. That
is, find P(B ∩ RB).
(c) Find the probability that the person prefers the black pieces, given that the person prefers
to play on the regular board. That is, find P(B|RB).
(d) Are the two events “the person prefers black” and “the person prefers the regular board”
mutually exclusive? Are they independent? Give supporting calculations.

Answer 1