Tomas’s favorite colors are \blue{\text{blue}}bluestart color #6495ed, start text, b, l, u, e, end text, end color #6495ed and \green{\text{green}}greenstart color #28ae7b, start text, g, r, e, e, n, end text, end color #28ae7b. He has \blue{\text{1 blue shirt}}1 blue shirtstart color #6495ed, start text, 1, space, b, l, u, e, space, s, h, i, r, t, end text, end color #6495ed, \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, \blue{\text{1 blue hat}}1 blue hatstart color #6495ed, start text, 1, space, b, l, u, e, space, h, a, t, end text, end color #6495ed, \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, \blue{\text{1 blue pair of pants}}1 blue pair of pantsstart color #6495ed, start text, 1, space, b, l, u, e, space, p, a, i, r, space, o, f, space, p, a, n, t, s, end text, end color #6495ed, 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.
Tomas selects one of these garments at random. Let AAA be the event that he selects a blue garment and let BBB be the event that he chooses a shirt.
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 Tomas selects a blue garment given that he has chosen a shirt is equal to the probability that Tomas selects a blue 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 Tomas selects a shirt given that he has chosen a blue garment is equal to the probability that Tomas selects a shirt.

(Choice C)
C
Events AAA and BBB are independent events.

(Choice D)
D
The outcome 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 Tomas selects a blue garment that is a shirt is equal to the probability that Tomas selects a blue garment multiplied by the probability that he selects a shirt.