A true-false test consists of 10 items. What is the probability that Chris gets 80% or more for the test?
I assume you mean by just guessing.
he must get 8 right, or 9 right or 10 right
= C(10,8)(1/2)^8 (1/2)^2 + C(10,9)(1/2)^9(1/2) + C(10,10) (1/2)^10
= (1/2)^10 ( 45 + 9 + 1)
= 55(1/2)^10
= 55/1024
not good, better study
Hi,
Can you please show the steps for
C(10,8)(1/2)^8 (1/2)^2 + C(10,9)(1/2)^9(1/2) + C(10,10) (1/2)^10
to
= (1/2)^10 ( 45 + 9 + 1)
I am a bit confused.
Thank you in advance :)
To determine the probability that Chris gets 80% or more in a true-false test, we need to know the number of items Chris answers correctly. However, you haven't provided any information about Chris's ability or knowledge. If we assume that Chris randomly guesses each item, we can use the binomial distribution to calculate the probability.
The binomial distribution is used when there are two possible outcomes (in this case, true or false) and each outcome has a fixed probability of occurring. In a true-false test, the probability of answering correctly by random guessing is 0.5 (assuming there is no penalty for guessing incorrectly).
Now, let's calculate the probability using the binomial distribution. In this case, Chris needs to answer at least 8 out of 10 questions correctly to achieve 80% or more.
The formula for the probability of achieving a certain number of successes in a binomial distribution is:
P(X = k) = (n Choose k) * p^k * (1-p)^(n-k)
Where:
n is the total number of trials (number of items in the test).
k is the desired number of successes (number of correctly answered items).
p is the probability of success (probability of answering a question correctly, which is 0.5 in this case).
Using this formula, we can calculate the probability of getting 8, 9, and 10 correct answers, and sum up those probabilities to get the final result.
P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10)
Let's calculate each probability:
P(X = 8) = (10 Choose 8) * (0.5)^8 * (1-0.5)^(10-8)
P(X = 9) = (10 Choose 9) * (0.5)^9 * (1-0.5)^(10-9)
P(X = 10) = (10 Choose 10) * (0.5)^10 * (1-0.5)^(10-10)
Finally, sum up these probabilities to get the final result:
P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10)
Please note that this calculation assumes random guessing, so the probability may be different if Chris has knowledge or skills that affect their ability to answer the questions correctly.