Question

A student takes a 20-question, multiple-choice exam with five choices for each question and guesses on each question. Find the probability of guessing at least 15 out of 20 correctly. Would you consider this event likely or unlikely to occur? Explain your answer.

Answer 1

Answer:

Step-by-step explanation:

Given that a student takes a 20-question, multiple-choice exam with five choices for each question and guesses on each question.

Since each question has 5 choices p = probability for success = pr for getting correct guess = 0.2

Each question is independent of the other and q= pr for failure =1-0.2=0.8

Hence we have X, no of correct questions in the test is binomial n =20 and p =0.2

the probability of guessing at least 15 out of 20 correctly

= $P(x=15)\\=20C15 (0.2)^{15} (0.8)^5$

<0.00001

So we can consider this event  unlikely to occur because the probability is almost zero.