Question

Here is a table showing all

52

cards in a standard deck.

												Face cards
Color	Suit	Ace	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten	Jack	Queen	King
Red	Hearts	A ♥	2 ♥	3 ♥	4 ♥	5 ♥	6 ♥	7 ♥	8 ♥	9 ♥	10 ♥	J ♥	Q ♥	K ♥
Red	Diamonds	A ♦	2 ♦	3 ♦	4 ♦	5 ♦	6 ♦	7 ♦	8 ♦	9 ♦	10 ♦	J ♦	Q ♦	K ♦
Black	Spades	A ♠	2 ♠	3 ♠	4 ♠	5 ♠	6 ♠	7 ♠	8 ♠	9 ♠	10 ♠	J ♠	Q ♠	K ♠
Black	Clubs	A ♣	2 ♣	3 ♣	4 ♣	5 ♣	6 ♣	7 ♣	8 ♣	9 ♣	10 ♣	J ♣	Q ♣	K ♣

Suppose one card is drawn at random from a standard deck.

(a)	Find the odds in favor of drawing a red seven.
(b)	Find the odds against drawing a face card.

Answer 1

B)

If A is an event and A’ is the complement of A, the odds against A are P(A’):P(A).

In this case, A is the event of drawing a face card

P(A) = 12/52

Since P(A) + P(A’) = 1:

P(A’) = 40/52

So, the odds against A are (40/52):(12/52) or

10:3

A)

If A is an event and A’ is the complement of A, the odds in favour of A are P(A):P(A').

In this case, A is the event of drawing a red 7.

P(A) = 2/52

Since P(A) + P(A’) = 1:

P(A’) = 50/52

So, the odds favour A are (2/52):(50/52) or

1:25