A student is writing a multiple choice test consisting of 40 questions, each of which provides four possible choices. He is certain that he has 16 questions correct. If he guesses for all of the remaining 24 questions, what is the probability that he will pass the test?
2007-05-18 07:27:48 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I'd add one thing to Dr D's answer. You have to use his formula for each score that would give you a passing score, THEN add up your results.
You're essentially figuring out how likely is it to guess a sequence of 8 correct answers and 16 incorrect (the (1/4)^8*(3/4)^16 part), then figuring out how many sequences you have that involve 8 correct, 16 incorrect (the C(24,8) part). In other words, you could guess question 1, 2, 3, 4, 5, 6, 7, and 8 correctly, you could guess questions 2, 3, 4, 5, 6, 7, 8 and 9 correctly, etc.
It's also possible to guess 9 correct answers, so you repeat the process for 9 correct, 15 incorrect.
With so many possible passing scores, this is a lot easier to do with Excel or MATLAB. Or notice that your probability has dropped practically to 0 by time you reach 13 correct and decide summing 8 through 12 is accurate enough.
2007-05-18 08:07:03 · answer #1 · answered by Bob G 6 · 0⤊ 0⤋
16 questions correct = 40%
if he guess for the next 24 questions then the probability that he is correct is 1/4 = 6 correct.
16 + 6 = 22 which is 55%
depending on the pass mark of the test, he will probably fail the exam
2007-05-18 08:19:00 · answer #2 · answered by hottawarrior - win lose or draw 5 · 0⤊ 0⤋
Assuming he has 16 correct, he must guess 24 ot the remaining questions. The odds are 1/4 that he will answer
any one of the remaining questions correctly so he can expect 6 additional correct answers. This will give him 22 correct answers out of 40 which is a grade of 55%.
55% is a failing grade. Assuming 70% is a passing grade, he must buck the odds and guess 1/2 of the remaining 24 questions correctly. The odds are at least 16 to 1 that he will fail.
2007-05-18 07:51:52 · answer #3 · answered by ironduke8159 7 · 0⤊ 1⤋
16 correct = 40%
Assuming 60% passes:
Then probability of answering remaining 24 by guessing correctly is 1/4 which yields 6 correct, which would add 15 points for a total of 55%, which is failing. Therefore I see the probability of passing as zero.
2007-05-18 07:45:12 · answer #4 · answered by Anonymous · 0⤊ 1⤋
Performing 16 corerct questions he is scoring 40% and guess work on the remeinder 24 questions will most proabably hit a few corerct ones I would say.
All depends upon what is the passig %age of teh test.
2007-05-18 07:34:32 · answer #5 · answered by shipdada 3 · 2⤊ 0⤋
What is the pass mark? If 60%, then that means he must get 24 questions right. That is 8 out of the remaining 24.
So you have a binomial distribution.
n = 24
p = 0.25
RTF: P(X >= 8)
P(X = x) = C(n,x) * 0.25^x * 0.75^(n-x)
Do it manually and add it up.
NOTE You cannot use a normal approximation for this one. n is too small.
2007-05-18 07:33:02 · answer #6 · answered by Dr D 7 · 3⤊ 0⤋
at the same time as brushing dip on some baking soda, (yellow field commonly in a kitchen) it may actually help any gum an infection. develop vit C and calsium. Rince mouth better typically. also undesirable tonsils can make undesirable breath so may even see a health care service, fairly if attending to many sore throats.
2016-11-04 08:54:06 · answer #7 · answered by Anonymous · 0⤊ 0⤋
he has a 1 in 65536 chance. Or a .001% chance of passing.
He has to get 8 more right if 60% is passing and there are 4 possible answers. So 1/(4^8) is the chance he will get it.
2007-05-18 07:52:02 · answer #8 · answered by pallarino47 3 · 0⤊ 1⤋