Dennis started reviewing a week before his exam. The probability of him passing the test given that he did not review at all is \(0.3\), and that chance increases by \(0.1\) for each day that he spends reviewing (maximum of \(6\) days). If on any given day, he has a even chance between reviewing and doing something else, what is the probability of passing the exam?

(Note: This problem was taken from my math statistics exam.)

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## Comments

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TopNewestMake cases. \[\begin{align} & 1) \ \text{He doesn't review at all and passes} \\ & 2) \ \text{He reviews one day and passes}\\ & \vdots\\ &\vdots \end{align}\]

This leads us to the following

\[P(\text{Dennis passes})=\dfrac{1}{640}\left(\displaystyle\sum_{n=0}^{6}\left[ \binom{6}{n} (3+n)\right]\right)=\dfrac{3}{5}=0.6\]

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