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7.4.3 Quiz: Conditional Probability
Question 1 of 10

Given:
[tex]\[
\begin{array}{l}
P(A) = 0.50 \\
P(B) = 0.80 \\
P(A \text{ and } B) = 0.20
\end{array}
\][/tex]

What is [tex]\( P(B \mid A) \)[/tex]?
A. 0.40
B. 0.25
C. 0.80
D. 0.30

Sagot :

GinnyAnswer
To determine [tex]\( P(B \mid A) \)[/tex], which is the conditional probability of event [tex]\( B \)[/tex] occurring given that event [tex]\( A \)[/tex] has occurred, we can use the formula for conditional probability:

[tex]\[ P(B \mid A) = \frac{P(A \text{ and } B)}{P(A)} \][/tex]

Let's break it down step-by-step:

1. Identify the given probabilities:
- [tex]\( P(A) = 0.50 \)[/tex]
- [tex]\( P(B) = 0.80 \)[/tex]
- [tex]\( P(A \text{ and } B) = 0.20 \)[/tex]

2. Apply the conditional probability formula:

[tex]\[ P(B \mid A) = \frac{P(A \text{ and } B)}{P(A)} \][/tex]

3. Substitute the known values into the formula:

[tex]\[ P(B \mid A) = \frac{0.20}{0.50} \][/tex]

4. Perform the division:

[tex]\[ P(B \mid A) = \frac{0.20}{0.50} = 0.4 \][/tex]

Therefore,
[tex]\[ P(B \mid A) = 0.40 \][/tex]

The correct answer is:

A. 0.40
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