If a student takes an exam containing 12 true or false questions. If the student guesses what is the probability that he will get exactly 8 questions right?
what is (1/2)^12 * 12!/8!4!
I get about 1/8
To find the probability of the student guessing exactly 8 questions right, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes can be calculated by finding the number of different ways the student can answer each question. Since each question has two possible answers (true or false), the total number of possible outcomes is 2 raised to the power of the number of questions. In this case, it would be 2^12 = 4096.
To find the number of favorable outcomes, we need to calculate the number of different ways the student can guess exactly 8 questions right out of 12. This can be done using the binomial coefficient formula, also known as "n choose k". The formula is:
C(n, k) = n! / (k! * (n-k)!)
where n is the total number of questions (12) and k is the number of questions answered correctly (8). The exclamation mark (!) denotes factorial, which means multiplying the number with all positive integers less than it.
Using the formula, the number of favorable outcomes is:
C(12, 8) = 12! / (8! * (12-8)!) = 495
Therefore, the probability of the student guessing exactly 8 questions right is the number of favorable outcomes divided by the total number of possible outcomes:
P(8 correct) = 495 / 4096 ≈ 0.1211 or 12.11% (rounded to four decimal places).