Question

A student takes a $32$-question multiple-choice exam, but did not study and randomly guesses each answer. Each question has three possible choices for the answer. Find the probability that the student guesses more than $75\%$of the questions correctly.

Short answer

The probability of getting quite $75\%$of the $32$ questions correct when randomly guessing is incredibly small and practically zero.

Step-by-step solution

Given information

A student takes a $32$-question multiple-choice exam, but didn't study and randomly guesses each answer.

Each question has three choices forthe solution. .

Explanation

X = number of questions answered correctly

$X~B(32,1/3)$

We have an interest in additional THAN questions$75\%of32$questions correct. $75\%of32$is $24$. we wish to seek out $P(x>24)$.

The event "more than 24" is that the complement of "less than or adequate to $24$."

• Using your calculator's distribution menu: $1–binomcdf(32,\frac{1}{3},24)$

• $P(x>24)=0$

• The probability of getting quite$75\%ofthe32$questions correct when randomly guessing is incrediblysmall and practically zero.