Marcus has a bag that contains
5
55 identically shaped boxes.
3
3start color #6495ed, start text, 3, end text, end color #6495ed of the boxes are
blue
bluestart color #6495ed, start text, b, l, u, e, end text, end color #6495ed, and
2
2start color #28ae7b, start text, 2, end text, end color #28ae7b are
green
greenstart color #28ae7b, start text, g, r, e, e, n, end text, end color #28ae7b.
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
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
A
AA be the event that he selects a blue box and
B
BB be the event that the box contains a prize.
Which of the following statements are true?
Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
P
(
A
|
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 Marcus selects a blue box given that he has chosen a box with a prize is equal to the probability that Marcus selects a blue box.

(Choice B)
B
P
(
B
|
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 Marcus selects a box with a prize given that he has chosen a blue box is equal to the probability that Marcus selects a box with a prize.

(Choice C)
C
Events
A
AA and
B
BB are independent events.

(Choice D)
D
The outcomes of events
A
AA and
B
BB are dependent on each other.

(Choice E)
E
P
(
A
and
B
)
=
P
(
A
)
⋅
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 Marcus selects a box that is blue and contains a prize is equal to the probability that Marcus selects a blue box multiplied by the probability that he selects a box with a prize.