Answer: the probability is 0.13
Step-by-step explanation:
First, each question has 5 options and only one is correct.
Then, selecting at random, the probability of getting a correct answer is equal to:
p = 1/5 = 0.20 (and the probability of getting it incorrect is p = 4/5 = 0.80)
Now, if out of 30 questions, we got 4 correct and 26 incorrect, the probability for a given combination is;
p = (0.20^4)*(0.80^26)
But we also need to multiply this by the total number of combinations.
This is we have 30 questions in total, and we can select 4 of them that will be the correct ones.
Now, if we have N objects in total, the number of different combinations of K elements out of those N elements is
In this case, N = 30 and K = 4.
Then the probability of getting exactly 4 correct answers is:
P = (0.20^4)*(0.80^26)*27,405 = 0.13