Suppose a biology student is about to take an exam that is entirely multiple choice, where...

Suppose a biology student is about to take an exam that is entirely multiple choice, where each question has 5 answer choices. This student only studied 60% of the material that is covered on this exam, so let us assume that there is a 60% chance that she knows the correct answer to any given question. If she does not know the answer, she will choose an answer at random.

a.If she answered a question on the exam correctly, what is the probability it was just because she guessed?

b. If the exam has a total of 40 questions on it, how many would you expect her to get wrong?

Solutions

Expert Solution

There are two possibilities with each question. Either the student knows the correct answer to the Q, which happens with a 60% probability. Another case is that she does not know. Even then, since she is selecting an answer at random out of the given choices, she has a 20% (1 in 5) chance of selecting the correct answer "by fluke". Hence, we can summarize this as

Thus we have obtained, using total probability, the chance that she gets an answer correct. This will be further used in the Conditional probability problem asked in first part. The event of guessing has been stated as not knowing in above analysis. Thus we can now conclude

For the second part, it is now as simple as the probability to getting an answer incorrect, times the number of questions. We have already obtained the probability to get correct answer as 0.68. Hence, the complementary probability is 0.32. We expect her to get 40 times 0.32 viz. 13 answers wrong (rounding off)

orchestra answered 1 year ago

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