Posted by **Scott** on Thursday, May 22, 2014 at 12:48pm.

In a multiple choice test that contains ten questions with each question having five possible answers, what is the probability that Colin will pass the test if he merely guesses at each question?

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**MathMate**, Thursday, May 22, 2014 at 9:59pm
Probability of getting the right answer for 1 question = 1 choice out of 5, or p=1/5.

Assuming independence among the 10 questions, probability of getting all 10 right = p^{10}

Probability of passing (getting 6 or more right out of 10) using binomial probabilities

=10C6*p^6q^4 + 10C7*p^7q^3 + 10C8*p^8q^2 + 10C9*p^9q + 10C10p^10

=(10752+1536+144+8+1)/9765625

= 12441/9765625

= 0.00127 approx.

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