Can someone explain how to do this probability question to me?

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SUMMARY

This discussion focuses on calculating probabilities involving two events, G and H, with given probabilities P(G) = 0.5, P(H) = 0.3, and P(G and H) = 0.1. The key calculation involves finding P(G or H^c) and the area of H\setminus G, which represents the part of event H that does not overlap with event G. The visual representation of these events as intersecting circles aids in understanding the relationships between the probabilities.

PREREQUISITES
  • Understanding of basic probability concepts, including union and intersection of events.
  • Familiarity with Venn diagrams for visualizing probabilities.
  • Knowledge of complementary events, specifically the concept of H^c.
  • Ability to perform basic arithmetic operations with probabilities.
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  • Study the principles of probability theory, focusing on union and intersection formulas.
  • Learn how to construct and interpret Venn diagrams for multiple events.
  • Explore the concept of complementary events and their applications in probability.
  • Practice solving probability problems involving multiple events and their intersections.
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Students studying probability theory, educators teaching statistics, and anyone looking to improve their understanding of event relationships in probability.

das1
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Let G and H be two events for which one knows that P(G) = 0.5, P(H) = 0.3, and P(G and H) = 0.1.

What is P(G or HC)?
 
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Draw $G$ and $H$ as intersecting circles. You know the area of $G$, the area of $H$ and the area of their intersection $G\cap H$. Can you find the area of $H\setminus G$ (that is, the part of $H$ that is not in $G$)? Then draw $G\cup H^c$ and think how it relates to $H\setminus G$.
 
That cleared it up, thanks
 

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