Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. ● G = card drawn is • E = card drawn is even-numbered a. b. P(G) = C. P(G|E) = green P(GE) = d. P(GUE)

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### Probability Exercise with Cards

#### Scenario:
Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.

#### Definitions:
- \( G \) = card drawn is green
- \( E \) = card drawn is even-numbered

#### Questions:
a. \( P(G) = \) _______

b. \( P(G|E) = \) _______

c. \( P(G \cap E) = \) _______

d. \( P(G \cup E) = \) _______

---

Use the above setup to fill in the probabilities for each question:

a. The probability that the card drawn is green \((P(G))\)

b. The probability that the card drawn is green given that it is even-numbered \((P(G|E))\)

c. The probability that the card drawn is both green and even-numbered \((P(G \cap E))\)

d. The probability that the card drawn is either green or even-numbered \((P(G \cup E))\)

Understanding these probabilities helps reinforce concepts like conditional probability, intersection, and union of events. Analyze the cards and complete the probabilities accordingly.
Transcribed Image Text:### Probability Exercise with Cards #### Scenario: Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. #### Definitions: - \( G \) = card drawn is green - \( E \) = card drawn is even-numbered #### Questions: a. \( P(G) = \) _______ b. \( P(G|E) = \) _______ c. \( P(G \cap E) = \) _______ d. \( P(G \cup E) = \) _______ --- Use the above setup to fill in the probabilities for each question: a. The probability that the card drawn is green \((P(G))\) b. The probability that the card drawn is green given that it is even-numbered \((P(G|E))\) c. The probability that the card drawn is both green and even-numbered \((P(G \cap E))\) d. The probability that the card drawn is either green or even-numbered \((P(G \cup E))\) Understanding these probabilities helps reinforce concepts like conditional probability, intersection, and union of events. Analyze the cards and complete the probabilities accordingly.
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