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

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To solve the probability question involving events G and H, the known probabilities are P(G) = 0.5, P(H) = 0.3, and P(G and H) = 0.1. To find P(G or HC), one can use the formula P(G or H) = P(G) + P(H) - P(G and H). The area of H not in G, or H\setminus G, can be calculated as P(H) - P(G and H), resulting in 0.2. Visualizing G and H as intersecting circles helps clarify the relationships between the areas, particularly when considering G∪H^c. Understanding these concepts simplifies the probability calculations.
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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
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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