laila guesses on all 20 questions of a multiple - choice test. each question has 4 answer choices. what is…

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?\n\n$p(success)=\frac{1}{4};p(failure)=\frac{3}{4}$\n\n$p(success)=\frac{1}{4};p(failure)=\frac{1}{2}$\n\n$p(success)=\frac{3}{4};p(failure)=\frac{1}{4}$\n\n$p(success)=1;p(failure)=0$

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?\n\n$p(success)=\frac{1}{4};p(failure)=\frac{3}{4}$\n\n$p(success)=\frac{1}{4};p(failure)=\frac{1}{2}$\n\n$p(success)=\frac{3}{4};p(failure)=\frac{1}{4}$\n\n$p(success)=1;p(failure)=0$

Answer

Explanation:

Step1: Define success probability

Success is getting a question right. With 4 answer - choices per question, the probability of getting a question right by guessing is the number of correct answers (1) divided by the total number of answers (4). So $P(\text{success})=\frac{1}{4}$.

Step2: Define failure probability

The sum of the probability of success and failure is 1. Let $P(\text{failure}) = x$. Then $P(\text{success})+x = 1$. Substituting $P(\text{success})=\frac{1}{4}$, we get $x=1 - \frac{1}{4}=\frac{3}{4}$.

Answer:

A. $P(\text{success})=\frac{1}{4};P(\text{failure})=\frac{3}{4}$