Imagine taking a 10-question true or false exam. You randomly guess at each question. Don't do any calculations, just tell me your first impressions
a). Is this a binomial setting?
b) How many question do you think you would get correct?
c). How surprised would you be if you passed ( 6 out of 10 correct or better) the exam?
d) How surprise would you be if you got an "A" on the exam (9 or 10 out of 10)?
ell, I will just do the problem
a yes
p(right) = .5, (1 -pright)=.5
b half of them, 5
10 trials
p(k) = C(n,k) p^k (1-p)^(n-k)
p(6)=C(10,6) .5^6 .5^4 =210*.015625*.0625 = .205
p(7) = 120*.5^7*.5^3 = .117
p(8) = 45*.5^8 *.5^2 = .044
p(9) = 10*.5^9*.5 = .0098
p(10) = 10*.5^10 = .0005
so prob of six through ten = sum = .376 is probability of passing
p(9)+p(10) = .0005+.044 = .045
a) Yes, this is a binomial setting. In a binomial setting, there are a fixed number of independent trials (in this case, 10 questions) and each trial has only two outcomes (true or false).
b) Since you are randomly guessing at each question, you would expect to get about 50% of the questions correct. So, you may expect to get around 5 questions correct, but it could vary since it is based on random guessing.
c) If you passed the exam by getting 6 or more questions correct, it would be somewhat surprising but not very surprising. Since you are randomly guessing, there is a chance that you could get more than 5 correct by sheer luck. However, the probability of passing the exam by randomly guessing is not very high either.
d) If you got an "A" on the exam by getting 9 or 10 questions correct, it would be extremely surprising. The probability of randomly guessing and getting 9 or 10 questions correct is very low. It would be highly unlikely to achieve such a high score by random guessing alone.
a) Yes, this is a binomial setting because there are only two possible outcomes for each question - true or false.
b) Since you are randomly guessing at each question, we can expect that you have a 50% chance of getting each question correct. Therefore, out of 10 questions, you would likely get around 5 correct.
c) If you randomly guess at each question, it would be quite surprising to pass the exam by getting 6 or more questions correct. While it is possible, the probability of achieving such a result by random guessing alone is relatively low. Therefore, passing the exam would be quite surprising.
d) Getting an "A" on the exam, which means getting 9 or 10 questions correct, would be extremely surprising if you are randomly guessing. The chances of getting such a high score without any knowledge or skill would be very slim. Thus, it would be highly unexpected to achieve this level of success by random guessing alone.