Occuring Events- Probabilities

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SUMMARY

The discussion centers on calculating probabilities related to drawing poker chips from a box containing two white, two red, and two blue chips. The events defined include A) both chips being the same color, B) both chips being red, and C) at least one chip being red or white. The correct identification of events is crucial, as A and B require listing specific pairs of chips rather than calculating probabilities. The valid outcomes for event A are {WW, BB, RR}, while event B is specifically {RR}.

PREREQUISITES
  • Basic understanding of probability theory
  • Familiarity with combinatorial counting methods
  • Knowledge of conditional probability notation
  • Ability to interpret and define events in probability contexts
NEXT STEPS
  • Study the concept of conditional probability, specifically P(A/B) and P(B/A^c)
  • Learn about combinatorial methods for counting outcomes in probability
  • Explore examples of defining events in probability problems
  • Practice with similar probability problems involving drawing without replacement
USEFUL FOR

This discussion is beneficial for students studying probability, educators teaching probability concepts, and anyone preparing for exams involving combinatorial probability scenarios.

n77ler
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Homework Statement


A box contains two white, two red, and two blue poker chips. Two chips are randomly chosen without replacement, and their colors are noted. Define the following events:
A) Both chips are of the same color
B)Both chips are red
C)At least one chip is red or white
Find P(A/B), P(B/A^c), P(B/C), P(A/C), P(C/A^c)


Homework Equations





The Attempt at a Solution


A) So at the start there are 6 chips, probability of pulling out the first one of any color would be 6/6 then there is one less in the bag but we now need the same color as we hauled out the first time. So if you have a red one out for example there are 5 chips left and only one is red so is it 1/5 chance?
 
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Wouldnt the answer be the same for both A and B ?
 
Do you understand what A and B ask? Neither A nor B asks for a probability. That is the last question in the problem (that is not labeled). A and B merely asks for a lists of the "events"- that is, a list of the pairs of chips that satisfy the conditions "two chips of the same color" for A and "two red chips" for B. No, the answers are not the same- and nothing that you said under "A)" has anything to do with the answer to A.
 
So for the first one it can be defined as {WW,BB,RR} because those are the chips that can satisfy the conditions?
 
Can someone please help me this is the easiest of 4 questions I have left I'm lost
 

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