Jason has a bag that contains 8
88 identically shaped boxes.
6
6start color #6495ed, start text, 6, 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.
3
of the blue boxes have a prize
3 of the blue boxes have a prizestart color #6495ed, start text, 3, 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.
Jason randomly selects a box from the bag. Let
A
AA be the event that he selects a box with a prize and
B
BB be the event that the box is green.
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 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.

(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 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.

(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 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.