Question

here is a table showing all 52 cards in a standard deck. suppose one card is drawn at random from a standard deck. (a) find the odds against drawing a queen. (b) find the odds in favor of drawing a black face card.

Explanation:

Step1: Calculate number of queens and non - queens

There are 4 queens in a 52 - card deck. So the number of non - queens is $52 - 4=48$.

Step2: Find odds against drawing a queen

The odds against an event $E$ is the ratio of the number of unfavorable outcomes to the number of favorable outcomes. For drawing a queen, the odds against is $\frac{48}{4}=\frac{12}{1}$, or 12:1.

Step3: Calculate number of black face cards and non - black - face cards

There are 6 black face cards (Jack, Queen, King of Spades and Jack, Queen, King of Clubs). The number of non - black - face cards is $52 - 6 = 46$.

Step4: Find odds in favor of drawing a black face card

The odds in favor of an event $E$ is the ratio of the number of favorable outcomes to the number of unfavorable outcomes. For drawing a black face card, the odds in favor is $\frac{6}{46}=\frac{3}{23}$, or 3:23.

Answer:

(a) 12:1
(b) 3:23