Question

You have a 5-questiontrue multiple -choice test. Each question has four choices. You don't know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly?

Answer 1

in 'n' trials for identical trials of an experiment, where only two possible outcomes exist i.e. success or failure and the probability of success is 'p' and probability of failure is 'q' then the probability of 'r' successes is given by
\[^{n} C _{r}p ^{r}q ^{n-r}\]
This is known as Bernoulli's Experiment.
Now we have 5 questions and we don't know any of the answers so we assume the situations of all the 5 questions to be similar.
also we have only 2 possible outcomes i.e. either the answer is correct or incorrect which means either success or failure.

Answer 2

Now the probability of success (getting the answer correct) is 1/4.
It is so because we have to guess the answer and we have 4 total outcomes i.e. option A, option B, Option C or Option D and we have only one favourable outcome (the correct answer). So the probability of success is 1/4.

Now, as u know there are only 2 possible outcomes(success or failure) so
p + q = 1 (total probability i.e. sum of all possible ouitcomes)
and since p = 1/4
therefore q = 3/4

Answer 3

The question demands exactly 3 successes......so put it in the formula and you can easily get the answer.

Answer 4

Just let me know if you didn't get any of it..