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.