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
 

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