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.

Answer 1

Answer: 0.774193548

Step-by-step explanation:

I intend to use the simplest method to solve this problem, without using any complex probability theorems but a very simple but absolutely correct technique.

We know Probability is defined as ;

P = (Number of Required Outcomes)/ (Number of Possible outcomes)

PLEASE NOTE THAT THE TECHNIQUE AM ABOUT TO USE MAKES ONE ASSUMPTION; All that is most important is that the student scores 75% exactly, and the method can continue iteratively.

NOW BACK TO SOLUTION

P = (Number of Required Outcomes)/ (Number of Possible outcomes)

FINDING REQUIRED OUTCOME

75% of 3 choice multiple exam consisting of 32 questions will be

75% of (32 × 3 )

= 0.75 of (96)

= 72.

FINDING POSSIBLE OUTCOMES

100% of (32 × 3)

= 1.00 of (96)

= 96

PROBABILITY OF THE STUDENT GUESSING 75% CORRECTLY IS

72/96 = 0.774193548

To get more than 75% we can iteratively determine the answer. But we know that the value will keep decreasing. I can define one formula for the iterative analysis.

[(O.75+0.01...............0.24) of 96 / (96)]