What is the probability of getting 80% or more of the questions correct on a 10-question true-false exam merely by guessing?
Binomial distribution with p = .5
p(10 right)
= c(10,10) .5^10 (.5)^0 =.5^10 = .000976
p( 9 right)
= c(10,9) .5^9 (.5)^1 = .00976
p(8 right)
= c(10,8) (.5)^8 (.5)^2 = 45*.5^10 = .04394
sum = .0547
I can't understand your way.... can u explain or do it another way
To find the probability of getting 80% or more of the questions correct on a 10-question true-false exam merely by guessing, we can use the concept of binomial probability.
The probability of getting a question correct by guessing is 0.5 (since there are two possible outcomes: true or false, and you have a 50% chance of guessing correctly). The probability of getting a question incorrect by guessing is also 0.5.
Let's break down the possible outcomes based on the number of questions answered correctly. We want to calculate the probability of getting 8, 9, or 10 questions correct.
To calculate the probability of getting exactly k questions correct out of n questions, we use the formula for binomial probability:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k questions correct.
- C(n, k) is the number of ways to choose k items from a set of n items. This is calculated using the combination formula: C(n, k) = n! / (k!(n-k)!)
- p is the probability of getting a single question correct (0.5 in this case).
- k is the number of questions answered correctly.
- n is the total number of questions (10 in this case).
To find the probability of getting 8, 9, or 10 questions correct, we can calculate the probability of each of these outcomes and sum them up:
P(X = 8) = C(10, 8) * 0.5^8 * 0.5^(10-8)
P(X = 9) = C(10, 9) * 0.5^9 * 0.5^(10-9)
P(X = 10) = C(10, 10) * 0.5^10 * 0.5^(10-10)
Finally, we can add up these probabilities:
P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10)
By evaluating these calculations, you'll find the probability of getting 80% or more of the questions correct on a 10-question true-false exam merely by guessing.