Question

A standard deck of cards has 52 cards. The 52 cards are divided into four suits: diamonds, clubs, hearts, and spades. Diamonds and hearts are red cards, and clubs and spades are black cards. Suppose you choose a card from the deck. Let event A
𝐴
be you choose a red card and event B
𝐵
you choose an ace. Determine P(A and B)
𝑃
(
𝐴

and

𝐵
)
, P(A)
𝑃
(
𝐴
)
, and P(B)
𝑃
(
𝐵
)
, and state whether events A
𝐴
and B
𝐵
are independent.

Enter the first three answers in fraction form. Reduce your answer.

(2 points)
P(A and B)=
𝑃
(
𝐴

and

𝐵
)
=
;
P(A)=
𝑃
(
𝐴
)
=
;
P(B)=
𝑃
(
𝐵
)
=
;
Enter 1 if events A
𝐴
and B
𝐵
are dependent. Enter 2 if events A
𝐴
and B
𝐵
are independent

Answer 1

P(A and B) = 1/26; P(A) = 1/2; P(B) = 1/13.
Since 1/26 = (1/2)(1/13), A and B are independent → enter 2.