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Let's solve the problem step by step.

### Part a: How many elements are there in the sample space?

You have 5 green cards, numbered 1 to 5, and 3 yellow cards, numbered 1 to 3. Since each card is distinct, the total number of cards is the sum of the green and yellow cards.

- Green cards: 5 (numbered 1, 2, 3, 4, 5)
- Yellow cards: 3 (numbered 1, 2, 3)

Total number of cards (sample space) = \( 5 + 3 = 8 \).

So, **the number of elements in the sample space is 8**.

### Part b: \( P(E) \) — The probability that the card drawn is even-numbered

The even-numbered cards from the deck are:
- Green: 2, 4
- Yellow: 2

So, there are 3 even-numbered cards.

The probability \( P(E) \) is the ratio of the number of favorable outcomes (even-numbered cards) to the total number of outcomes (total cards):

\[
P(E) = \frac{\text{Number of even-numbered cards}}{\text{Total number of cards}} = \frac{3}{8}
\]

Now, let's round this to 4 decimal places:

\[
P(E) = 0.3750
\]

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Would you like further details or have any questions about the solution?

Here are 5 follow-up questions to deepen understanding:
1. What is the probability of drawing a green card (\( P(G) \))?
2. What is the probability of drawing a yellow card (\( P(\text{Yellow}) \))?
3. What is the probability of drawing a card that is both green and even-numbered?
4. How would the probabilities change if the number of yellow cards increased to 5?
5. What is the complement of \( P(E) \) (the probability of drawing an odd-numbered card)?

**Tip:** Probabilities are always between 0 and 1. A probability of 1 means the event is certain, while a probability of 0 means it is impossible.

A special deck of cards has 5 green cards, and 3 yellow cards. The green cards are numbered 1, 2, 3, 4, and 5. The yellow cards are numbered 1, 2, and 3. The cards are well shuffled and you randomly draw one card. G = card drawn is green, E = card drawn is even-numbered. a. How many elements are there in the sample space? b. P(E) = ? (Round to 4 decimal places)

This problem involves calculating the number of elements in a sample space and determining the probability of drawing an even-numbered card from a special deck containing 5 green cards and 3 yellow cards. Learn how to solve this probability question step by step.

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