Marcus has a bag that contains 555 identically shaped boxes. \blue{\text{$3$}}3start color #6495ed, start text, 3, end text, end color #6495ed of the boxes are \blue{\text{blue}}bluestart color #6495ed, start text, b, l, u, e, end text, end color #6495ed, and \green{\text{$2$}}2start color #28ae7b, start text, 2, end text, end color #28ae7b are \green{\text{green}}greenstart color #28ae7b, start text, g, r, e, e, n, end text, end color #28ae7b. \blue{\text{$2$ of the blue boxes have a prize}}2 of the blue boxes have a prizestart color #6495ed, start text, 2, space, o, f, space, t, h, e, space, b, l, u, e, space, b, o, x, e, s, space, h, a, v, e, space, a, space, p, r, i, z, e, end text, end color #6495ed , and \green{\text{$1$ of the green boxes has a prize}}1 of the green boxes has a prizestart color #28ae7b, start text, 1, space, o, f, space, t, h, e, space, g, r, e, e, n, space, b, o, x, e, s, space, h, a, s, space, a, space, p, r, i, z, e, end text, end color #28ae7b. Marcus randomly selects a box from the bag. Let AAA be the event that he selects a blue box and BBB be the event that the box contains a prize.

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 Jason selects a box with a prize given that he has chosen a green box is equal to the probability that Jason selects a box with a prize.

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 Jason selects a green box given that he has chosen a box with a prize is equal to the probability that Jason selects a green box.

C. Events AAA and BBB are independent events.

E. 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 Jason selects a box that contains a prize and is green is equal to the probability that Jason selects a box with a prize multiplied by the probability that he selects a green box.

the answer is ! ?

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