A teacher gave a 10 question multiple choice quiz. Each question had 4 choices to select from. If the student completely guessed on every problem, what is the probability that they make a score of exactly a 50% (i.e. 5 exactly 5 questions correct)? (PDF)

a)0.0264

b)0.2461

c)0.0584

d)0.9803

Step-by-step explanation: First we must consider the number of different groups of 5 questions that can be answered correctly from the 10. This is given by 10C5, ie how many ways of choosing 5 from 10. 10C5=252.

We also know that the probability of guessing a question correctly is 1/4=0.25. We want this to occur 5 times, so we have 0.25^5.

Clearly the probability of guessing wrongly on each question is 0.75. We also require this to happen 5 times, giving 0.75^5.

So the answer is, 10C5 times 0.25^5 times 0.75^5 =0.0584 to 4dp

A teacher gave a 10 question multiple choice quiz. Each question had 4 choices to select from. If the student completely guessed on every problem, what is the probability that they make a score of exactly a 50% (i.e. 5 exactly 5 questions correct)? (PDF) a)0.0264 b)0.2461 c)0.0584 d)0.9803

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A teacher gave a 10 question multiple choice quiz. Each question had 4 choices to select from. If the student completely guessed on every problem, what is the probability that they make a score of exactly a 50% (i.e. 5 exactly 5 questions correct)? (PDF)

a)0.0264

b)0.2461

c)0.0584

d)0.9803