Lorinda has 101010 books on her bookshelf. \blue{\text{$6$}}6start color #6495ed, start text, 6, end text, end color #6495ed of
these books have \blue{\text{blue covers}}blue coversstart color #6495ed, start text, b, l, u, e, space, c, o, v, e, r, s, end text, end color #6495ed, and \red{\text{$4$}}4start color #df0030, start text, 4, end text, end color #df0030 have \red{\text{red covers}}red coversstart color #df0030, start text, r, e, d, space, c, o, v, e, r, s, end text, end color #df0030. \blue{\text{$3$}}3start color #6495ed, start text, 3, end text, end color #6495ed of the blue books are \blue{\text{mystery novels}}mystery novelsstart color #6495ed, start text, m, y, s, t, e, r, y, space, n, o, v, e, l, s, end text, end color #6495ed, and \blue{\text{$3$}}3start color #6495ed, start text, 3, end text, end color #6495ed are \blue{\text{fantasy novels}}fantasy novelsstart color #6495ed, start text, f, a, n, t, a, s, y, space, n, o, v, e, l, s, end text, end color #6495ed. \red{\text{$2$}}2start color #df0030, start text, 2, end text, end color #df0030 of the red books are \red{\text{mystery novels}}mystery novelsstart color #df0030, start text, m, y, s, t, e, r, y, space, n, o, v, e, l, s, end text, end color #df0030, and \red{\text{$2$}}2start color #df0030, start text, 2, end text, end color #df0030 are \red{\text{fantasy novels}}fantasy novelsstart color #df0030, start text, f, a, n, t, a, s, y, space, n, o, v, e, l, s, end text, end color #df0030. Lorinda closes her eyes and randomly selects a book from her bookshelf. Let AAA be the event that she selects a blue book and BBB be the event that the book is a fantasy novel. Which of the following statements are true? Choose all answers that apply: Choose all answers that apply: (Choice A) A P(A\text{ | }B)=P(A)P(A | B)=P(A)P, left parenthesis, A, start text, space, vertical bar, space, end text, B, right parenthesis, equals, P, left parenthesis, A, right parenthesis, the conditional probability that Lorinda selects a blue book given that she has chosen a fantasy novel is equal to the probability that Lorinda selects a blue book. (Choice B) B P(B\text{ | }A)=P(B)P(B | A)=P(B)P, left parenthesis, B, start text, space, vertical bar, space, end text, A, right parenthesis, equals, P, left parenthesis, B, right parenthesis, the conditional probability that Lorinda selects a fantasy novel given that she has chosen a blue book is equal to the probability that Lorinda selects a fantasy novel. (Choice C) C Events AAA and BBB are independent events. (Choice D) D The outcomes of events AAA and BBB are dependent on each other. (Choice E) E P(A\text{ and }B)=P(A) \cdot P(B)P(A and B)=P(A)⋅P(B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, equals, P, left parenthesis, A, right parenthesis, dot, P, left parenthesis, B, right parenthesis, the probability that Lorinda selects a book that is blue and a fantasy novel is equal to the probability that Lorinda selects a blue book multiplied by the probability that she selects a fantasy novel.
