A student takes a true-false test exam with 10 questions. If the student guesses all ten questions, find the probability he gets 7 or 8 right.
p(x=7) + p(x=8)
(.5)^7(.5)^3 + (.5)^8(.5)^2
I have the correct answers which are .117+.044= .161
But when I calculate the answer on the calculator, I get a different answer. Am I putting this into the calculator wrong?
To calculate the probability of getting 7 or 8 questions right on a true-false test, you need to use the binomial probability formula.
The formula for the probability of getting exactly x successes in n independent trials, each with the same probability of success (p), is:
P(x) = C(n, x) * p^x * (1 - p)^(n - x)
Where C(n, x) represents the number of combinations of n items taken x at a time, which can be calculated as:
C(n, x) = n! / (x! * (n - x)!)
For the given problem, we have n = 10 (the number of questions) and p = 0.5 (the probability of guessing correctly).
To calculate P(x=7) + P(x=8), we can use the above formula:
P(x=7) = C(10, 7) * (0.5)^7 * (1 - 0.5)^(10 - 7)
P(x=8) = C(10, 8) * (0.5)^8 * (1 - 0.5)^(10 - 8)
Now, let's calculate the probabilities:
P(x=7) = 10! / (7! * (10 - 7)!) * (0.5)^7 * (0.5)^3 = 0.117
P(x=8) = 10! / (8! * (10 - 8)!) * (0.5)^8 * (0.5)^2 = 0.044
P(x=7) + P(x=8) = 0.117 + 0.044 = 0.161
So, the correct answer is indeed 0.161.
If you're getting a different answer on your calculator, make sure you're performing the calculations correctly, especially with the combination function (C(n, x)). Also, double-check that you're using the correct values for n, x, and p in the formula.