A test is composed of six multiple choice questions where each question has 4 choices. If the answer choices for each question are equally likely, find the probability of answering 3 OR 4 questions correctly.
0.131836
0.032959
0.004639
0.164795
I would get the chances of getting 3 questions right and the chances of getting 4 questions right, and then add the two chances together.
To find the probability of answering 3 OR 4 questions correctly, we need to calculate the probability of answering 3 questions correctly and add it to the probability of answering 4 questions correctly.
The probability of answering 3 questions correctly can be calculated using the binomial probability formula:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k)
Where:
- n is the number of trials (number of questions in this case) = 6
- k is the number of successes (number of questions answered correctly)
- p is the probability of success (probability of answering a question correctly) = 1/4
Using this formula:
P(X = 3) = (6 C 3) * (1/4)^3 * (3/4)^(6 - 3)
= (6! / (3! * (6-3)!)) * (1/4)^3 * (3/4)^3
= 20 * (1/64) * (27/64)
= 20/64
= 5/16
Similarly, the probability of answering 4 questions correctly can be calculated:
P(X = 4) = (6 C 4) * (1/4)^4 * (3/4)^(6 - 4)
= (6! / (4! * (6-4)!)) * (1/4)^4 * (3/4)^2
= 15 * (1/256) * (9/16)
= 135/4096
To find the probability of answering 3 OR 4 questions correctly, we add the probabilities:
P(3 OR 4) = P(X = 3) + P(X = 4)
= 5/16 + 135/4096
= 820/4096
= 64/256
= 0.25
Therefore, the correct answer is 0.25.