You pick a card at random, put it back, and then pick another card at random. 2 3 What is the probability of picking a number greater than 1 and then picking a prin Simplify your answer and write it as a fraction or whole number.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Probability: Independent Events**

**Question:**  
You pick a card at random, put it back, and then pick another card at random.

**Card Options:**  
1, 2, 3

**Question:**  
What is the probability of picking a number greater than 1 and then picking a prime number? Simplify your answer and write it as a fraction or whole number.

**Instructions:**  
1. Click **Submit** to check your answer.

**Explanation:**  
1. There are 3 cards, all picked with replacement.
2. Identify the event of picking a number greater than 1 and a prime number:
   - The numbers greater than 1 are 2 and 3.
   - The prime numbers in this set are also 2 and 3.

**Steps to Solve:**
1. Calculate the probability of picking a number greater than 1:
   - Possible outcomes greater than 1 are 2 and 3 (2 out of 3).
   - Probability = \( \frac{2}{3} \).

2. Calculate the probability of picking a prime number:
   - Possible prime numbers are 2 and 3 (2 out of 3).
   - Probability = \( \frac{2}{3} \).

3. Using the rule of independent events, multiply the probabilities:
   - Probability = \( \frac{2}{3} \times \frac{2}{3} = \frac{4}{9} \).

**Answer:**  
The probability of picking a number greater than 1 and then picking a prime number is \( \frac{4}{9} \).
Transcribed Image Text:**Probability: Independent Events** **Question:** You pick a card at random, put it back, and then pick another card at random. **Card Options:** 1, 2, 3 **Question:** What is the probability of picking a number greater than 1 and then picking a prime number? Simplify your answer and write it as a fraction or whole number. **Instructions:** 1. Click **Submit** to check your answer. **Explanation:** 1. There are 3 cards, all picked with replacement. 2. Identify the event of picking a number greater than 1 and a prime number: - The numbers greater than 1 are 2 and 3. - The prime numbers in this set are also 2 and 3. **Steps to Solve:** 1. Calculate the probability of picking a number greater than 1: - Possible outcomes greater than 1 are 2 and 3 (2 out of 3). - Probability = \( \frac{2}{3} \). 2. Calculate the probability of picking a prime number: - Possible prime numbers are 2 and 3 (2 out of 3). - Probability = \( \frac{2}{3} \). 3. Using the rule of independent events, multiply the probabilities: - Probability = \( \frac{2}{3} \times \frac{2}{3} = \frac{4}{9} \). **Answer:** The probability of picking a number greater than 1 and then picking a prime number is \( \frac{4}{9} \).
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