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total number of outcomes = 2 ^10 = 16 * 16 *2euro wrote:In a quiz, a contestant is asked 10 questions, to which he should answer true or false. He should answer at least 8 questions correctly to move to the next level of the quiz. If he answers all the questions, what is the probability that he does not proceed to the next level?
a) 7/128
b) 17/28
c) 121/128
d) 11/28
e) 10/128
Official Answer is C
The solution in the post above is surely the intended solution here, but the wording of this question is awful. Where is it from? In order to answer this question, you need to know the probability that the contestant answers each question correctly. Perhaps the contestant understands the content of the quiz extremely well, and has a nearly 100% chance of answering each question correctly (and thus has a very high probability of advancing to the next level), or perhaps the contestant is guessing at random, and has a 50% chance of answering each question correctly (and thus has a low probability of advancing). Obviously the question designer intends for the probability of a correct answer to be 50% on each question, but that needs to be stated in the question itself; otherwise it can't be answered.euro wrote:In a quiz, a contestant is asked 10 questions, to which he should answer true or false. He should answer at least 8 questions correctly to move to the next level of the quiz. If he answers all the questions, what is the probability that he does not proceed to the next level?
a) 7/128
b) 17/28
c) 121/128
d) 11/28
e) 10/128
Official Answer is C
In the very first line, the problem reads "...to which he should answer true or false." It is also mentioned in the problem that the contestant attempts all the 10 questions.Ian Stewart wrote: The solution in the post above is surely the intended solution here, but the wording of this question is awful. Where is it from? In order to answer this question, you need to know the probability that the contestant answers each question correctly. Perhaps the contestant understands the content of the quiz extremely well, and has a nearly 100% chance of answering each question correctly (and thus has a very high probability of advancing to the next level), or perhaps the contestant is guessing at random, and has a 50% chance of answering each question correctly (and thus has a low probability of advancing). Obviously the question designer intends for the probability of a correct answer to be 50% on each question, but that needs to be stated in the question itself; otherwise it can't be answered.
My Explanation:euro wrote:In a quiz, a contestant is asked 10 questions, to which he should answer true or false. He should answer at least 8 questions correctly to move to the next level of the quiz. If he answers all the questions, what is the probability that he does not proceed to the next level?
a) 7/128
b) 17/28
c) 121/128
d) 11/28
e) 10/128
Official Answer is C
That doesn't mean the contestant has a 0.5 probability of answering each question correctly. If the contestant knew the quiz content perfectly, and had a 100% chance of answering each question correctly, the answer would clearly be 0. If instead he or she had a 0.9 probability of answering each question correctly, the answer would beeuro wrote: In the very first line, the problem reads "...to which he should answer true or false."
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