Question
Suppose that $A$ and $B$ are mutually exclusive events, with $P(A)>0$ and $P(B)<1 .$ Are $A$ and $B$ independent? Prove your answer.
Step 1
This means that they cannot occur at the same time. Mathematically, this is represented as $A \cap B = \emptyset$, which means the intersection of $A$ and $B$ is an empty set. Show more…
Show all steps
Your feedback will help us improve your experience
Manisha Sarker and 84 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
Assume that two events A and B are mutually exclusive and independent. Prove that P(B) = 0 if P(A) = 1/9
-Suppose that $A$ and $B$ are independent events such that the probability that neither occurs is $a$ and the probability of $B$ is $b$. Show that $P(A)=\frac{1-b-a}{1-b}$.
Probability
Two Laws of Probability
Suppose two events $A$ and $B$ are independent, with $P(A) \neq 0$ and $P(B) \neq 0 .$ By working through the following steps, you'll see why two independent events are not mutually exclusive. (a) What formula is used to compute $P(A \text { and } B) ?$ Is $P(A \text { and } B) \neq 0 ?$ Explain. (b) Using the information from part (a), can you conclude that events $A$ and $B$ are not mutually exclusive?
Elementary Probability Theory
Some Probability Rules—Compound Events
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD