The problem in the uploaded image asks the following:

Task:

For the experiment of drawing a single card from a standard 52-card deck:

1. (a) Find the probability of the event where the card is not a three.
2. (b) Find the odds (in simplified form) in favor of the card not being a three.

Solution:

(a) Probability of not drawing a three:

1. In a standard 52-card deck, there are 4 threes (one from each suit: hearts, diamonds, clubs, spades).
2. The number of cards that are not threes is: $52 - 4 = 48$
3. The probability of not drawing a three is therefore: $P(\text{not a three}) = \frac{\text{Number of not-three cards}}{\text{Total number of cards}} = \frac{48}{52}$
4. Simplify the fraction: $\frac{48}{52} = \frac{12}{13}$

Answer for (a): The probability is $\frac{12}{13}$.

(b) Odds in favor of not drawing a three:

1. Odds are calculated as: $\text{Odds in favor of an event} = \frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}$
2. The number of favorable outcomes (not a three) is $48$, and the number of unfavorable outcomes (a three) is $4$.
3. The odds are: $\text{Odds} = \frac{48}{4} = 12 : 1$

Answer for (b): The odds in simplified form are $12 : 1$.

Final Answers:

• (a) $\frac{12}{13}$
• (b) $12 : 1$

Would you like a deeper explanation or help with related problems?

Here are five related questions you might consider:

1. How are odds and probabilities connected mathematically?
2. What are the odds against drawing a three in this situation?
3. If you draw two cards without replacement, what is the probability that neither is a three?
4. How do probabilities change if the deck includes jokers?
5. What is the probability of drawing a three of hearts specifically?

Tip: Always simplify probabilities and odds to their lowest terms for clarity and correctness!