Question

It is a discrete math problem about probability:

You flip a nickel (5 cents coin) and roll a six-sided die.
Points are assigned as follows. The nickel showing heads is worth 1 point and the
nickel showing tails is worth 5 points. The points for the die correspond simply to
the number on its upper surface. Each outcome is equally likely and we define the
following events.

A: The sum of points is greater than 7. B: The sum of points is even.

(a) Define the sample space in set notation.
(b) Write down A and p(A).
(c) Write down B and p(B).
(d) Write down A ∩ B and p(A ∩ B).
(e) Write down A ∪ B and p(A ∪ B).
(f) Write down p(A) in terms of p( ¯ A).

(g) How are p(A), p(B), p(A ∩ B), and p(A ∪ B) related (equation)?
(h) Are A and B mutually exclusive?
(i) Write down p(A|B).
(j) Are A and B independent?
(k) Write down p(B|A).
(l) Write down p(A ∩ B) in terms of p(A) and p(B).

Answer 1