You need to use binomial probability formula to determine what is the probability that the student to get 5 questions out of 5 correct, hence:

`P(r) = C_n^r*p^r*q^(n-r)`

Notice that the 5 questions are 4 choice questions, hence the probability to get one correct choice out of 4 is: `p = 1/4 = 0.25` .

You need to remember that `p+q=1 =gt q = 1 - 1/4 = 3/4 = 0.75`

Hence, the probability not to get a correct answer is of `3/4=0.75` .

Evaluating the probability that the student to get 5 correct answers out of 5 such that:

`P(5) = C_5^5*(0.25)^5*(0.75)^(5-5)`

`P(5) = 1*0.0009*1 =gt P(5) = 0.0009`

Hence, the probability that the student to get 5 answers correct is of 0.0009.

The student determines the correct answer by choosing a ball from a box that has 4 balls marked with the options A, B, C and D. The probability that a randomly picked ball has the right answer is 0.25.

In a test that has 5 questions the probability that using the system gives all answers right is (0.25)^5 = 9.765*10^-4

The probability that  she gets all five answers right using her system is  9.765*10^-4