How Do You Calculate the Intersection Probability for Mutually Exclusive Events?

I'm confused about how to do thisIn summary, the probability of event A and B occurring together is 0.1 based on the given information. For the second problem, the probability of waiting exactly 15 minutes for the bus is 1/30, and the probability of waiting between 15 and 20 minutes is 5/30.
  • #1
Quincy
228
0

Homework Statement


Consider events A, B, and C such that P (A) = P (B) = P (C) = 0.2, A and C are mutually exclusive, B and C are mutually exclusive, and P (A ∪ B ∪ C) = 0.5. Give the value of P (A ∩ B), providing justification for your answer.


Homework Equations





The Attempt at a Solution


If A & C and B & C are mutually exclusive, and if P(A U B U C) = 0.5, then P(A U B) = 0.3. And if P(A) = P(B) = 0.2, then P(A ∩ B) = 0.1.
 
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  • #3
What about this one:

A bus arrives at a station every day at a random time between 1:00 PM and 1:30 PM.

a) What is the probability that the person has to wait exactly 15 minutes for the bus?

b) What is the probability that the person has to wait between 15 and 20 minutes for the bus?

a) 1/30

b) 5/30 -- I'm not really sure if this one is right
 

Related to How Do You Calculate the Intersection Probability for Mutually Exclusive Events?

What is probability?

Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

What is the difference between probability and statistics?

Probability is the theoretical branch of mathematics that deals with the likelihood of events occurring. Statistics, on the other hand, is the application of mathematical methods to analyze and interpret data and make predictions about future events.

What are the two main types of probability?

The two main types of probability are theoretical (or classical) probability and experimental (or empirical) probability. Theoretical probability is based on mathematical principles and assumes that all outcomes are equally likely. Experimental probability is based on actual observations and data.

What is a normal distribution?

A normal distribution is a bell-shaped curve that represents a set of data whose values are symmetrically distributed around the mean. It is commonly used in statistics to describe the distribution of real-world data.

How can probability and statistics be applied in real life?

Probability and statistics are used in a wide range of fields, including science, finance, engineering, and social sciences. They can be used to make predictions, analyze trends, and make informed decisions based on data. Some examples of applications include weather forecasting, risk analysis, and market research.

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