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? (Round to 4 decimal places) b. P(E)=
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? (Round to 4 decimal places) b. P(E)=
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![### Probability Exercise: Special Deck of Cards
A special deck of cards consists of 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.
Let:
- \( G \) = card drawn is green
- \( E \) = card drawn is even-numbered
#### Questions:
a. How many elements are in the sample space?
\[ \_\_\_\_ \]
b. What is \( P(E) \)?
\[ \_\_\_\_ \] (Round to 4 decimal places)
### Explanation:
1. **Sample Space Calculation:**
- The total number of cards = 5 (green) + 3 (yellow) = 8.
Therefore, the number of elements in the sample space is 8.
2. **Probability Calculation:**
- To calculate \( P(E) \), first identify the even-numbered cards:
- Green cards: 2, 4
- Yellow cards: 2
- There are 3 even-numbered cards in total.
- The probability \( P(E) \) is the number of even-numbered cards divided by the total number of cards:
\[ P(E) = \frac{\text{Number of even-numbered cards}}{\text{Total number of cards}} = \frac{3}{8} = 0.3750\]
Thus, the probability \( P(E) \) rounded to four decimal places is 0.3750.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11f84057-ddc6-4a16-833f-eeebb801b1ce%2Fbcdc6635-443f-4bd3-a67e-538498a128b0%2Fsi0vi8i_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Exercise: Special Deck of Cards
A special deck of cards consists of 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.
Let:
- \( G \) = card drawn is green
- \( E \) = card drawn is even-numbered
#### Questions:
a. How many elements are in the sample space?
\[ \_\_\_\_ \]
b. What is \( P(E) \)?
\[ \_\_\_\_ \] (Round to 4 decimal places)
### Explanation:
1. **Sample Space Calculation:**
- The total number of cards = 5 (green) + 3 (yellow) = 8.
Therefore, the number of elements in the sample space is 8.
2. **Probability Calculation:**
- To calculate \( P(E) \), first identify the even-numbered cards:
- Green cards: 2, 4
- Yellow cards: 2
- There are 3 even-numbered cards in total.
- The probability \( P(E) \) is the number of even-numbered cards divided by the total number of cards:
\[ P(E) = \frac{\text{Number of even-numbered cards}}{\text{Total number of cards}} = \frac{3}{8} = 0.3750\]
Thus, the probability \( P(E) \) rounded to four decimal places is 0.3750.
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