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Rewrite the following statements as equations using mathematical notation:

- The probability of rain is low
- The probability of rain given that it is cloudy is high
- The probability of you having an umbrella given it is raining is much greater than the probability of you having an umbrella in general.
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\begin{aligned}
&P(\operatorname{rain})=\text { low } \\
&P(\text { rain } \mid \text { cloudy })=\text { high } \\
&P(\text { umbrella } \mid \text { rain }) \gg P(\text { umbrella })
\end{aligned}
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