45/1024 = 4.4%, approx.
0.05 I think is the answer
The probability that the student will pass is; P(pass) = P(10) + P(9) + P(8) = [10C10 + 10C9 + 10C8] / (.5)10 = 56/1024 ~ ~ 0.0547 ~ 5.47% where nCr = n!/[r!(n-r)!]
Psychology researches do use probability samples, so the question is based on false premises.
50:50
The probability this student will fail is the same as the probability that some other student will flip a fair coin 20 times and get less than 8 heads, i.e., more than 12 tails. There are 2^20 possible different-looking sequences of 20 coinflips, which we assume all have equal probability. Of those sequences, 1 has no heads at all, 20 have exactly 1 head, 190 have exactly 2 heads, ... and 77520 have exactly 7 heads. So we sum up all those possible ways to fail and we get ... ... ... I'm assuming that the student answers randomly, flipping a fair (50:50) coin on each question to choose "true" or "false". In that special case, it doesn't matter how many of those twenty questions are true or how many are false. (If the student answers randomly by flipping an unfair coin, say a 25:75 coin, then it does matter how many of those questions are true -- I'll let you figure that one out).
5 out of 10
50%
7/128, or about 5.5% The student has a 1/2 probability of getting each question correct. The probability that he passes is the probability that he gets 10 correct+probability that he gets 9 correct+probability that he gets 8 correct: P(passes)=P(10 right)+P(9 right)+P(8 right)=[(1/2)^10]+[(1/2)^10]*10+[(1/2)^10]*Combinations(10,2)=[(1/2)^10](1+10+45)=56/1024=7/128.
0.05 I think is the answer
The probability that the student will pass is; P(pass) = P(10) + P(9) + P(8) = [10C10 + 10C9 + 10C8] / (.5)10 = 56/1024 ~ ~ 0.0547 ~ 5.47% where nCr = n!/[r!(n-r)!]
Total number of different ways he can fill out the answer sheet = 210 = 1,024 .He passes the test if he gets zero wrong, one wrong, or two wrong.Number of ways to get zero wrong = 1.Number of ways to get exactly one wrong = 10.Number of ways to get exactly two wrong = 45.Total number of ways to get exactly 0, 1, or 2 wrong = (1 + 10 + 45) = 56.Probability of passing = (56) / (1,024) = 5.47%(rounded)
The probability of getting at least 1 answer correct = 1 - Probability of getting all answers correct.So in your case it for be P(at least 1 answer correct) = 1 - 1/256where 256 is your sample space, |S| = 2^8.
Psychology researches do use probability samples, so the question is based on false premises.
50:50
If you answer randomly, 1 in 8.
The probability this student will fail is the same as the probability that some other student will flip a fair coin 20 times and get less than 8 heads, i.e., more than 12 tails. There are 2^20 possible different-looking sequences of 20 coinflips, which we assume all have equal probability. Of those sequences, 1 has no heads at all, 20 have exactly 1 head, 190 have exactly 2 heads, ... and 77520 have exactly 7 heads. So we sum up all those possible ways to fail and we get ... ... ... I'm assuming that the student answers randomly, flipping a fair (50:50) coin on each question to choose "true" or "false". In that special case, it doesn't matter how many of those twenty questions are true or how many are false. (If the student answers randomly by flipping an unfair coin, say a 25:75 coin, then it does matter how many of those questions are true -- I'll let you figure that one out).
That depends a lot on the specific circumstances, of how you guess. For instance, if a test has true/false questions, the probability is 1/2; if it is a multiple-choice question with 4 options, the probability is 1/4; if there are 6 options, the probability is 1/6, etc.; if you have to calculate a number (and it is NOT a multiple choice question), the probability is rather low, indeed.