Question

A multiple choice test has 10​ questions, each of which has 4 possible​ answers, only one of which is correct. If​ Judy, who forgot to study for the​ test, guesses on all​ questions, what is the probability that she will answer exactly 3 questions​ correctly? Round your answer to four decimal places.

Answer 1

Answer:

0.2503

Step-by-step explanation:

To solve this , we use the Bernoulli trial equation.

Now, there are 10 questions with 4 options each. The total number of options is thus = 10 × 4 = 40 options

There are only 10 correct answers however. The probability of picking a correct answer is thus 1/4 or 0.25

Now we know there are 30 wrong options. The probability of picking a wrong option is 30/40 or 0.75

To answer 3 questions correctly, it means she would answer 7 wrongfully.

Now to complete the parameters for the bernoulli trial, we know she is making 3 correct choices. Now the number of ways to select three correct choices out of 10 is 10C3

Computing the Bernoulli trial, we have :

(10C3) × (0.25)^3 × (0.75)^10

= 0.2503