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First time using this website, but I will post the remaining given in the problem.

You are able to answer 3 questions correctly, and you will guess the remaining 4. (total 7 questions). There are 4 choices to each problem. Find the probability you will pass the exam by guessing the remaining problems.

I understand that to solve this problem, we use the binomial theorem which would be $$\sum_{i=4}^{7} \binom{7}{i}\frac{a^i}{b^{7-i}}$$

My question is, what is a and b?

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  • $\begingroup$ How many questions must be answered correctly to pass the exam? $\endgroup$ Commented Apr 4, 2016 at 2:35

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You only fail if you guess all of the four remaining answers incorrectly.

The probability of guessing any one of the four incorrectly is 3/4. So what's the probability of guessing all four incorrectly? (They are independent events).

Once you know the probability $P_{f}$ of failing, the probability of passing is $P_p = 1 - P_f$.

Does this help?

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