Answered: 3. A retailer sells two brands of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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$### Probability of Selecting Two Batteries of the Same Brand **Question:** A retailer sells two brands of batteries that experience indicates are equal in demand. If he stocks two of each brand (which means he has four batteries in his store), what is the probability that a customer seeking to purchase two batteries, purchases the same brand? Options: - ( ) 1/3 - ( ) 2/3 - ( ) 1/2 - ( ) 1/4 --- This question requires calculating the probability of a customer purchasing two batteries of the same brand from a store that has an equal stock of two different brands. **Explanation:** Consider the combinations possible when selecting 2 batteries from 4, where there are 2 batteries each of Brand A and Brand B. 1. **Possible Combinations:** - AA (both batteries from Brand A) - BB (both batteries from Brand B) - AB (one battery from Brand A and one from Brand B) - BA (one battery from Brand B and one from Brand A) Since the combinations AB and BA are identical in probability (due to the symmetry in selection), we combine them, leaving us with 3 unique possibilities: AA, BB, and AB. 2. **Favorable Outcomes:** - The favorable outcomes for purchasing two batteries of the same brand are AA and BB. Since there are a total of 3 unique combinations, and 2 are favorable, we calculate the probability as follows: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of unique combinations}} = \frac{2}{3} \] **Answer Options:** - ( ) 1/3 - ( ) 2/3 - ( ) 1/2 - ( ) 1/4 Thus, the probability that a customer seeking to purchase two batteries will get two of the same brand is $ \frac{2}{3} $. **Correct Answer:** $ \frac{2}{3} $$

Transcribed Image Text:### Probability of Selecting Two Batteries of the Same Brand **Question:** A retailer sells two brands of batteries that experience indicates are equal in demand. If he stocks two of each brand (which means he has four batteries in his store), what is the probability that a customer seeking to purchase two batteries, purchases the same brand? Options: - ( ) 1/3 - ( ) 2/3 - ( ) 1/2 - ( ) 1/4 --- This question requires calculating the probability of a customer purchasing two batteries of the same brand from a store that has an equal stock of two different brands. **Explanation:** Consider the combinations possible when selecting 2 batteries from 4, where there are 2 batteries each of Brand A and Brand B. 1. **Possible Combinations:** - AA (both batteries from Brand A) - BB (both batteries from Brand B) - AB (one battery from Brand A and one from Brand B) - BA (one battery from Brand B and one from Brand A) Since the combinations AB and BA are identical in probability (due to the symmetry in selection), we combine them, leaving us with 3 unique possibilities: AA, BB, and AB. 2. **Favorable Outcomes:** - The favorable outcomes for purchasing two batteries of the same brand are AA and BB. Since there are a total of 3 unique combinations, and 2 are favorable, we calculate the probability as follows: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of unique combinations}} = \frac{2}{3} \] **Answer Options:** - ( ) 1/3 - ( ) 2/3 - ( ) 1/2 - ( ) 1/4 Thus, the probability that a customer seeking to purchase two batteries will get two of the same brand is $ \frac{2}{3} $. **Correct Answer:** $ \frac{2}{3} $

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