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# A Probability Problem

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.)

3 years ago

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Make 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

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

- 3 years ago