Question 5
Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.
and and .
not Round to 4 decimals.
Question Help: Video Message instructor

Ask by Kirk Best. in the United States

Jan 23,2025

Question

Question 5
Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.
and and .
not Round to 4 decimals.
Question Help: Video Message instructor

Ask by Kirk Best. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To find $$ P(\text{not } B \mid A) $$, we'll use the definition of conditional probability:

$$
P(\text{not } B \mid A) = \frac{P(A \cap \text{not } B)}{P(A)}
$$

**Given:**
- $$ P(A) = 0.5 $$
- $$ P(B) = 0.4 $$
- $$ P(A \cap B) = 0.10 $$

**Step 1: Find $$ P(A \cap \text{not } B) $$**

We know that:
$$
P(A) = P(A \cap B) + P(A \cap \text{not } B)
$$

So,
$$
P(A \cap \text{not } B) = P(A) - P(A \cap B) = 0.5 - 0.10 = 0.40
$$

**Step 2: Calculate $$ P(\text{not } B \mid A) $$**

$$
P(\text{not } B \mid A) = \frac{P(A \cap \text{not } B)}{P(A)} = \frac{0.40}{0.5} = 0.8
$$

**Rounded to four decimal places:**
$$
P(\text{not } B \mid A) = 0.8000
$$

**Answer:**  
$$ P(\text{not } B \mid A) = 0.8000 $$
$$ P(\text{not } B \mid A) = 0.8000 $$