Test consist of 10 multiple choice questions each having 4 possible answers one being correct. you guessed all 10 what is the probability of getting less than 30%
To find the probability of getting less than 30% (which means getting less than 3 questions correct) when guessing all 10 multiple-choice questions with 4 possible answers each, we can use the binomial probability formula.
The binomial probability formula is:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k successes.
- C(n, k) is the combination formula, which represents the number of ways to choose k items from a set of n items.
- p is the probability of success in a single trial.
- n is the total number of trials.
In this case, n (total number of trials) is 10, p (the probability of guessing correctly) is 1/4 (since there are 4 possible answers and only one correct answer), and we want to find the probability of getting less than 3 successes (k < 3).
Therefore, we need to calculate the following probabilities:
P(X=0) + P(X=1) + P(X=2)
Using the binomial probability formula, we can calculate each individual probability and then sum them up to find the final probability.
To calculate the probability of getting less than 30% correct on a 10-question multiple-choice test where each question has 4 possible answers (one being correct), we need to determine how many correct answers would correspond to less than 30%.
Since each question has 4 possible answers and only one is correct, the probability of guessing the correct answer to a question is 1/4, or 25%.
To find the probability of getting less than 30% correct, we need to find the cumulative probability of guessing 0, 1, 2, or 3 correct answers out of 10.
To calculate the cumulative probability, we can add up the individual probabilities for each scenario. Let's calculate:
P(Guessing 0 correct answers) = (1/4)^0 * (3/4)^10 = 0.0001409
P(Guessing 1 correct answer) = (1/4)^1 * (3/4)^9 * 10 = 0.002111
P(Guessing 2 correct answers) = (1/4)^2 * (3/4)^8 * 45 = 0.01474
P(Guessing 3 correct answers) = (1/4)^3 * (3/4)^7 * 120 = 0.04915
Adding up these probabilities, we get:
P(Less than 30% correct) = 0.0001409 + 0.002111 + 0.01474 + 0.04915
= 0.0661419
Therefore, the probability of getting less than 30% correct on a 10-question multiple-choice test is approximately 0.066 or 6.6%.