Let's solve the problem based on the image you provided.

Part (a): Probability of drawing an Ace or Queen

• A standard deck of 52 cards has 4 aces and 4 queens, giving us a total of $4 + 4 = 8$ cards that are either an ace or a queen.
• The probability $P$ of drawing an ace or a queen is the ratio of favorable outcomes to total outcomes:

$P(\text{Ace or Queen}) = \frac{\text{Number of Aces or Queens}}{\text{Total Cards}} = \frac{8}{52} = \frac{2}{13}$

Part (b): Odds in favor of drawing an Ace or Queen

• The odds in favor of an event are given by the ratio of favorable outcomes to unfavorable outcomes. There are 8 favorable outcomes (aces or queens) and $52 - 8 = 44$ unfavorable outcomes (all other cards).

Thus, the odds in favor of drawing an ace or queen are:

$\text{Odds in favor} = \frac{\text{Favorable Outcomes}}{\text{Unfavorable Outcomes}} = \frac{8}{44} = \frac{2}{11}$

So, the odds in favor are $2 : 11$.

Final Answers:

• (a) The probability is $\frac{2}{13}$.
• (b) The odds in favor are $2 : 11$.

Would you like more details or have any questions?

Here are five related questions:

1. What is the probability of drawing a king or a jack from a standard deck?
2. How do the odds against drawing a face card compare to the odds in favor of it?
3. What are the odds of drawing a card that is a diamond?
4. How do you convert probability to odds?
5. How do the odds change if jokers are included in the deck?

Tip: To find the odds in favor of an event, remember it's the ratio of favorable to unfavorable outcomes, not the total number of outcomes like in probability.