SOLUTION: In a true or false assignment of six questions you are obliged to get at least four correct to pass. If you guess the answer to the questions, what are the probabilities that: a.

Question 1132890: In a true or false assignment of six questions you are obliged to get at least four correct to pass. If you guess the answer to the questions, what are the probabilities that:
a. you pass
b. you get at least 50% of the answers correct; and
c. you get no more than two correct?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability of getting the answer correct on any single question is .5.
the probability of getting the answer wrong on any single question is 1 - .5 = .5
you have an equal chance of getting the question right or wrong.

this is a binomial distribution type problem.

the formula is p(x) = p^x * q^(n-x) * c(n,x)

the calculations are shown in the following spreadsheet printout.

$$$

the total probability is 1 as it should always be.

your solutions are in the spreadsheet printout.

probability of passing is getting 4 or 5 or 6 correct.
probability of getting at least half right is getting 3 or 4 or 5 or 6 correct.
probability of getting mo more than 2 correct is probability of getting 0 or 1 or 2 correct.

c(n,x) is equal to n! / (x! * (n-x!))

it's the number of ways you can get a set of x elements out of a set of n elements where order of the elements within the set is not important.

order is not important means that different orders of the same elements in the set are counted as one set.

for example:

the set of abc can have 6 different orders within the set.
they would be abc, acb, bac, bca, cab, cba.
when order is not important, they would be counted as one set because all the sets contain the same elements.
when order is important, they would be counted as 6 different sets.
they have the same elements but they are in a different order, therefore counted as different sets because order is important.

the c(n,x) formula assumes order is not important.

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