Chapter 1.1, Problem 3E

Draw one card at random from a standard deck of cards. The sample space S is the collection of the 52 cards. Assume that the probability set function assigns $\frac{1}{52}$ to each of the 52 outcomes. Let

A = {x: x is a jack, queen. or king}.

B = {x:x is a 9.10 or jack and x is red}.

C = {x:x is a club},

D = {x: x is a diamond, a heart, or a spade}.

Find $\left(\text{a}\right)P\left(A\right),\left(\text{b}\right)P\left(A\cap B\right),\left(\text{c}\right)P\left(A\cup B\right),\left(\text{d}\right)P\left(C\cup D\right),$ and (e) $P\left(C\cap D\right)$.