There are 3 apples and 5 oranges in a bag. Determine each probability. 5. Selecting 2 apples when they are chosen at random without replacement 6. Selecting an orange, then an apple when they are chosen at random without replacement

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Probability Exercise: Apples and Oranges**

*Scenario:* 
There are 3 apples and 5 oranges in a bag. Determine each probability.

**Problems:**

1. Selecting 2 apples when they are chosen at random without replacement.
   
   ______________________________________

2. Selecting an orange, then an apple when they are chosen at random without replacement.

   ______________________________________

---

**Explanation:**

1. **Selecting 2 apples without replacement:**

   To calculate the probability of selecting 2 apples from a bag containing 3 apples and 5 oranges without replacement, use the combination formula to determine the number of ways to select 2 apples from 3, divided by the number of ways to select any 2 fruits from 8 (3 apples + 5 oranges).

2. **Selecting an orange, then an apple without replacement:**

   To find this probability, calculate the probability of selecting an orange first, and then calculate the probability of selecting an apple given that an orange has already been removed from the bag. Multiply these two probabilities together to get the final result.

---

**Note:** Ensure to handle each step methodically, considering the changes in the total count of fruits after each selection due to the "without replacement" condition.
Transcribed Image Text:**Probability Exercise: Apples and Oranges** *Scenario:* There are 3 apples and 5 oranges in a bag. Determine each probability. **Problems:** 1. Selecting 2 apples when they are chosen at random without replacement. ______________________________________ 2. Selecting an orange, then an apple when they are chosen at random without replacement. ______________________________________ --- **Explanation:** 1. **Selecting 2 apples without replacement:** To calculate the probability of selecting 2 apples from a bag containing 3 apples and 5 oranges without replacement, use the combination formula to determine the number of ways to select 2 apples from 3, divided by the number of ways to select any 2 fruits from 8 (3 apples + 5 oranges). 2. **Selecting an orange, then an apple without replacement:** To find this probability, calculate the probability of selecting an orange first, and then calculate the probability of selecting an apple given that an orange has already been removed from the bag. Multiply these two probabilities together to get the final result. --- **Note:** Ensure to handle each step methodically, considering the changes in the total count of fruits after each selection due to the "without replacement" condition.
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