Binomial distribution

Suppose a student has a 50% chance of scoring a perfect score on an exam with randomly selected questions. Each student will be provided 5 attempts.

a) Compute and plot the probability distribution for the number of perfect scores over the 5 attempts.

b) What is the probability that a student will score a perfect score in exactly 2 out of the 5 attempts?

c) What is the probability that a student will score a perfect score in at least 2 out of the 5 attempts?

Geometric distribution

Suppose a student has a 50% chance of scoring a perfect score on an exam with randomly selected questions. The student has to repeatedly take the exam until he/she achieves a perfect score.

a) Compute and plot the probability distribution for number of failures before scoring a perfect score. The student will only go for a maximum of 10 attempts before giving up.

b) What is the probability that the student will score a perfect score on the third attempt?

c) What is the probability that the student will score a perfect score in at most three attempts?