The Professor's Response
Hi professor,
I got number #24 wrong in section 4.4. these are my numbers but I think they are mixed up ?
n=50
x=4
p=.35
q=.65
See the professor's answer below.
Hi Tufic,
In Binomial probability, n = the number of trials, so in this case it represents the number of problems we will take a guess on. You are correct to label n = 50.
We are looking for the probability that we get X successes. X represents the number of successes we want to have (note: a success isn't necessarily something positive). In this case, the problem says we want to know the likelihood of missing only 35 questions. This means for us missing a question is a success, and we want to know the probability that we miss 35 questions. This means X = 35 because 35 missed questions would be 35 successes.
Now this next part is important: if we define a success as missing a question, p = the probability we have a success in a single trial. This means to find p, we need to determine the probability that we miss a single question when we take a guess on one. Well, the problem says we have four answer choices for each question. This means the chance we guess incorrectly is P(missed question) = # of wrong answer options/ total number of answer options. This should be P(missed question) = 3 / 4, because there are 3 wrong answer choices for every question and four total answer choices for each one.
Lastly, our q = 1 - p, so in this case, that is q = 1 - 3/4 = 1/4.
This answer to the problem becomes: 50 C 35 * (3/4)^35 * (1/4)^15 (note: we have 15 as the exponent for the 1/4 because if we miss 35 questions, we get 15 correct out of 50).
Hope that helps,
Professor McGuckian