Question
Let $A$ and $B$ be two events in a sample space $S$ such that $P(A)=.4, P(B)=.6$, and $P(A \cap B)=.3$. Finda. $P(A \mid B)$b. $P(B \mid A)$
Step 1
We are given that $P(A \cap B) = 0.3$ and $P(B) = 0.6$. So, we have: $P(A \mid B) = \frac{0.3}{0.6} = \frac{1}{2} = 0.5$ Show more…
Show all steps
Your feedback will help us improve your experience
Sanchit Jain and 73 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let $A$ and $B$ be two events in a sample space for which $\mathrm{P}(A)=2 / 3$, $\mathrm{P}(B)=1 / 6$, and $\mathrm{P}(A \cap B)=1 / 9$. What is $\mathrm{P}(A \cup B) ?$
Suppose that $P(A)=.4$ and $P(A \cap B)=.12$. a. Find $P(B \mid A)$. b. Are events $A$ and $B$ mutually exclusive? c. If $P(B)=.3,$ are events $A$ and $B$ independent?
Probability and Probability Distribution
Independence, Conditional Probability, and the Multiplication Rule
For two events $A$ and $B, P(A)=.4, P(B)=.2,$ and $P(A \cap B)=.1$ a. Find $P(A \mid B)$. b. Find $P(B \mid A)$. c. Are $A$ and $B$ independent events?
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD