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PROPABILITY

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. Steve is a student taking a statistic course. Steve does not revise his notes before class, does not do homework and regularly misses class. Steve wants to rely on luck to pass the next test. The test consist of 10 multiple choice questions each question has 5 possible answers only one (one in five) of which is correct. Steve plans to guess the answer to each question.

What is the possibility that Steve gets:

1.2. At most 3 answers correct?

1.3. At least 2 answers correct?

Aug 19, 2019

$$\text{This is straightforward application of the binomial distribution}\\ p[\text{k answers correct}] = \dbinom{10}{k} \left(\dfrac 1 5\right)^k \left(\dfrac 4 5\right)^{10-k}\\~\\ p[0] = \left(\dfrac 4 5\right)^{10}\\ p[0\leq k \leq 3] = \sum \limits_{k=0}^3 p[k]\\ p[2\leq k \leq 10] = 1 - p[0\leq k \leq 1]= 1- p[0]-p[1]\\~\\ \text{I leave the plug and chug to you}$$