However, a student who knew only 32 out of 80 questions could guess randomly on the remaining 48 questions, and expect to come very close to the required 44 correct answers; so a student with knowledge at only the 40% level (whatever that means) might expect to pass, as long as there is no penalty for incorrect answers. -----Original Message----- From: math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com [mailto:math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com]On Behalf Of Henry Baker Sent: Monday, May 15, 2006 3:07 PM To: math-fun Subject: Re: [math-fun] California Math Exit Exam I didn't really set up this posting correctly. In California, we now (are supposed to) have an "exit exam" for high school students which sets standards for graduation. http://www.cde.ca.gov/ta/tg/hs/ The math portion of the test is approx. 80 questions, each of which is multiple choice with 4 choices. A radio talk show host here in Los Angeles was carrying on about how easy it should be to pass this examination, since it required only a 55% score to pass. If I've done _my_ math correctly, a completely random answer sheet with 20 questions would pass with a probability of ~ 1/254; with 40 questions would pass with a probability of ~ 1/20560, with 60 questions would pass with a probability of ~ 1/1467711, and with 80 questions would pass with a probability of ~ 10^-8. So, our random student would have to take the test on the order of 10 million times to have a good probability of passing it. So monkeys with typewriters probably aren't going to pass. At 08:42 PM 5/14/2006, Henry Baker wrote:

Here's another question to add to the California Exit Exam for high school students in mathematics:

If there are 80 questions on this test, and each of the 80 questions has 4 choices, what is the probability that someone could pass (>= 55%) [oops, first answer the question of how many questions out of a total of 80 questions 55% is] the test, if for each question he chose one of the 4 answers at random (p=25% for each answer).

Alternatively, assuming that the test preparers aren't insane, what is the probability that someone could pass the test by always choosing the "A" answer for each question?

Extra credit: using this probability, estimate the number of times one should take the test to raise the probability of passing it at least once to 80%.

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