MATH SOLVE

4 months ago

Q:
# A student guesses on every question of a multiple-choice test that has 6 questions, each with 3 possible answers. What is the probability that the student will get at least 4 of the questions right?

Accepted Solution

A:

Answer: The probability that the student will get at least 4 of the questions right is 0.0823044.
Step-by-step explanation:
For each question we have 3 choices. So,total choices will be :
[tex]3\times3\times3\times3\times3\times3=729[/tex]
Getting 4 correct means, 4 corrects and two wrongs
Now, as there are 3 answer choices, out of which only one will be correct, so 2/3 is the probability if a question is answered wrong.
And 1/3 is the probability if a question is answered correctly.
Hence, we can consider this probability :
[tex]P=(2/3)*(2/3)*(1/3)*(1/3)*(1/3)*(1/3)[/tex] = 4/729
=> P = 0.00548696
We can select any combination of 2 from 6 for being wrong, so we will multiply P by (6,2)=6!/(2!*4!) = 15
So the answer is P*15 =[tex]0.00548696*15=0.0823044[/tex]
The probability that the student will get at least 4 of the questions right is 0.0823044.