Ad, Category: Homework 57,95/100 paints EDorm aseng inem Current learning objective: The Addition Rule Question 28 Practice similar questions Pres Next Score: 0 of 2 points In a box of assorted cookies, $$ 32 \% $$ contain chocolate and $$ 15 \% $$ contain nuts. In the box, $$ 12 \% $$ contain both chocolate and nuts. Sean is allergic to both chocolate and nuts. Find the probability that a cookie contains chocolate or nuts (he can't eat it). 0.29 Find the probability that a cookie does not contain chocolate or nuts (he can eat it). 0.71

Question

UpStudy AI · Accepted Answer

It looks like you're working on a probability problem using the **Addition Rule**. Let's walk through the problem step by step to ensure clarity and accuracy.

### **Problem Statement:**
In a box of assorted cookies:
- **32%** contain chocolate.
- **15%** contain nuts.
- **12%** contain both chocolate and nuts.

Sean is allergic to both chocolate and nuts.

**Questions:**
1. **Find the probability that a cookie contains chocolate *or* nuts (Sean can't eat it).**
2. **Find the probability that a cookie does *not* contain chocolate or nuts (Sean can eat it).**

### **Solution:**

#### **1. Probability that a cookie contains chocolate or nuts (Sean can't eat it):**

To find the probability that a cookie contains **chocolate or nuts**, we use the **Addition Rule** for probabilities:

$$
P(\text{Chocolate or Nuts}) = P(\text{Chocolate}) + P(\text{Nuts}) - P(\text{Chocolate and Nuts})
$$

Plugging in the values:

$$
P(\text{Chocolate or Nuts}) = 0.32 + 0.15 - 0.12 = 0.35
$$

**So, the probability is **$$ \boxed{0.35} $$** or 35%.**

#### **2. Probability that a cookie does not contain chocolate or nuts (Sean can eat it):**

This is the complement of the first probability. To find this, subtract the probability that a cookie contains chocolate or nuts from 1:

$$
P(\text{Neither Chocolate nor Nuts}) = 1 - P(\text{Chocolate or Nuts}) = 1 - 0.35 = 0.65
$$

**So, the probability is **$$ \boxed{0.65} $$** or 65%.**

### **Summary:**
1. **Probability Sean can't eat a cookie (contains chocolate or nuts):** **35%** $$(0.35)$$
2. **Probability Sean can eat a cookie (does not contain chocolate or nuts):** **65%** $$(0.65)$$

### **Possible Reason for Score of 0:**
It appears there might have been a miscalculation in your answers:
- You answered **0.29** for **P(Chocolate or Nuts)**, but the correct calculation is **0.35**.
- Consequently, for **P(Neither)**, the correct answer is **0.65**, not **0.71**.

Ensure to carefully apply the Addition Rule and double-check your arithmetic to avoid such discrepancies.

### **Additional Tip:**
Always remember that when calculating the probability of "A or B," you need to subtract the overlap $$ P(A \text{ and } B) $$ to avoid double-counting the cases where both events occur.

If you have any more questions or need further clarification, feel free to ask!
The probability that a cookie contains chocolate or nuts is 0.35, and the probability that a cookie does not contain chocolate or nuts is 0.65.

Solución de tutoría real

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Probability Questions