Bilal’s favorite colors are \red{\text{red}}redstart color #df0030, start text, r, e, d, end text, end color #df0030 and \green{
\text{green}}greenstart color #28ae7b, start text, g, r, e, e, n, end text, end color #28ae7b. He has \red{\text{1 red shirt}}1 red shirtstart color #df0030, start text, 1, space, r, e, d, space, s, h, i, r, t, end text, end color #df0030, \green{\text{1 green shirt}}1 green shirtstart color #28ae7b, start text, 1, space, g, r, e, e, n, space, s, h, i, r, t, end text, end color #28ae7b, \red{\text{1 red hat}}1 red hatstart color #df0030, start text, 1, space, r, e, d, space, h, a, t, end text, end color #df0030, \green{\text{1 green scarf}}1 green scarfstart color #28ae7b, start text, 1, space, g, r, e, e, n, space, s, c, a, r, f, end text, end color #28ae7b, \red{\text{1 red pair of pants}}1 red pair of pantsstart color #df0030, start text, 1, space, r, e, d, space, p, a, i, r, space, o, f, space, p, a, n, t, s, end text, end color #df0030, and \green{\text{1 green pair of pants}}1 green pair of pantsstart color #28ae7b, start text, 1, space, g, r, e, e, n, space, p, a, i, r, space, o, f, space, p, a, n, t, s, end text, end color #28ae7b. Bilal selects one of these garments at random. Let AAA be the event that he selects a green garment and let BBB be the event that he chooses a scarf. 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 Bilal selects a green garment given that he has chosen a scarf is equal to the probability that Bilal selects a green garment. (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 Bilal selects a scarf given that he has chosen a green garment is equal to the probability that Bilal selects a scarf. (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 Bilal selects a garment that is green and is a scarf is equal to the probability that Bilal selects a green garment multiplied by the probability that he selects a scarf.
