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In an aquarium, there are 10 large fish and 5 small fish. Half of the large fish are red. One fish is selected at random. Find the probability that it is a large, red fish.

In an aquarium, there are 10 large fish and 5 small fish. Half of the large fish are red. One fish is selected at random. Find the probability that it is a large, red fish.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Problem Statement:** In an aquarium, there are 10 large fish and 5 small fish. Half of the large fish are red. One fish is selected at random. Find the probability that it is a large, red fish. Write your answer as a fraction. **Solution:** To find the probability of selecting a large, red fish, follow these steps: 1. **Determine the total number of fish in the aquarium:** - Large fish: 10 - Small fish: 5 - Total fish: \(10 + 5 = 15\) 2. **Determine the number of large, red fish:** - Half of the large fish are red. - Number of large, red fish: \(\frac{1}{2} \times 10 = 5\) 3. **Calculate the probability:** - Probability of selecting a large, red fish = \(\frac{\text{Number of large, red fish}}{\text{Total number of fish}}\) - Probability = \(\frac{5}{15} = \frac{1}{3}\) **Answer:** The probability of selecting a large, red fish is \(\frac{1}{3}\).
Transcribed Image Text:**Problem Statement:** In an aquarium, there are 10 large fish and 5 small fish. Half of the large fish are red. One fish is selected at random. Find the probability that it is a large, red fish. Write your answer as a fraction. **Solution:** To find the probability of selecting a large, red fish, follow these steps: 1. **Determine the total number of fish in the aquarium:** - Large fish: 10 - Small fish: 5 - Total fish: \(10 + 5 = 15\) 2. **Determine the number of large, red fish:** - Half of the large fish are red. - Number of large, red fish: \(\frac{1}{2} \times 10 = 5\) 3. **Calculate the probability:** - Probability of selecting a large, red fish = \(\frac{\text{Number of large, red fish}}{\text{Total number of fish}}\) - Probability = \(\frac{5}{15} = \frac{1}{3}\) **Answer:** The probability of selecting a large, red fish is \(\frac{1}{3}\).
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