Dairy Delight offers a free ice cream every time that the saleperson does not greet the customer with a smile. Last year Dairy Delight gave away free ice cream 3.8% of the time. What is the probability of randomly selecting 3 customers from last year who all received a free ice cream? Round the answer to 6 decimals.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Probability Problem: Dairy Delight Ice Cream Giveaways**

**Scenario:**
Dairy Delight offers a free ice cream every time that the salesperson does not greet the customer with a smile. Last year, Dairy Delight gave away free ice cream 3.8% of the time. 

**Problem:**
What is the probability of randomly selecting 3 customers from last year who all received a free ice cream? Round the answer to 6 decimals.

**Solution:**
To solve the problem, we use the probability of a single customer receiving a free ice cream, which is 0.038 (3.8%).

Since we are looking for the probability that all three customers were given free ice cream, we calculate as follows:

\[ 
P(\text{3 free ice creams}) = 0.038 \times 0.038 \times 0.038 
\]

\[ 
P(\text{3 free ice creams}) = (0.038)^3 
\]

**Calculation:**

\[
(0.038)^3 = 0.000054872
\]

**Answer:**
The probability of selecting 3 customers who all received a free ice cream is approximately 0.000055 (rounded to 6 decimals). 

**Note:** Ensure all calculations consider the rounding to maintain consistency and accuracy.
Transcribed Image Text:**Probability Problem: Dairy Delight Ice Cream Giveaways** **Scenario:** Dairy Delight offers a free ice cream every time that the salesperson does not greet the customer with a smile. Last year, Dairy Delight gave away free ice cream 3.8% of the time. **Problem:** What is the probability of randomly selecting 3 customers from last year who all received a free ice cream? Round the answer to 6 decimals. **Solution:** To solve the problem, we use the probability of a single customer receiving a free ice cream, which is 0.038 (3.8%). Since we are looking for the probability that all three customers were given free ice cream, we calculate as follows: \[ P(\text{3 free ice creams}) = 0.038 \times 0.038 \times 0.038 \] \[ P(\text{3 free ice creams}) = (0.038)^3 \] **Calculation:** \[ (0.038)^3 = 0.000054872 \] **Answer:** The probability of selecting 3 customers who all received a free ice cream is approximately 0.000055 (rounded to 6 decimals). **Note:** Ensure all calculations consider the rounding to maintain consistency and accuracy.
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