Question

laila guesses on all 20 questions of a multiple - choice test. each question has 4 answer choices. what is the probability of a success and a failure for this experiment?

p(success) = 1/4, p(failure) = 3/4

p(success) = 1/4, p(failure) = 1/2

p(success) = 3/4, p(failure) = 1/4

p(success) = 1, p(failure) = 0

Explanation:

Step1: Define success and failure probabilities

Success is getting a question right. Since there are 4 answer - choices per question and only 1 is correct, the probability of success $P(\text{success})$ is the number of favorable outcomes (1 correct answer) divided by the number of total outcomes (4 answer - choices). So, $P(\text{success})=\frac{1}{4}$.

Step2: Calculate the probability of failure

The probability of failure $P(\text{failure})$ is the complement of the probability of success. Using the formula $P(\text{failure}) = 1 - P(\text{success})$. Substituting $P(\text{success})=\frac{1}{4}$, we get $P(\text{failure})=1-\frac{1}{4}=\frac{3}{4}$.

Answer:

$P(\text{success})=\frac{1}{4}, P(\text{failure})=\frac{3}{4}$ (corresponding to the first option in the multiple - choice list)