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?\\(\boldsymbol{\circ}\\) \\(p(\text{success}) = \frac{1}{4}; p(\text{failure}) = \frac{3}{4}\\)\\(\boldsymbol{\circ}\\) \\(p(\text{success}) = \frac{1}{4}; p(\text{failure}) = \frac{1}{2}\\)\\(\boldsymbol{\circ}\\) \\(p(\text{success}) = \frac{3}{4}; p(\text{failure}) = \frac{1}{4}\\)\\(\boldsymbol{\circ}\\) \\(p(\text{success}) = 1; p(\text{failure}) = 0\\)

Explanation:

Step1: Calculate success probability

Each question has 1 correct out of 4 choices, so $P(\text{success}) = \frac{1}{4}$.

Step2: Calculate failure probability

Failure is all non-success outcomes, so $P(\text{failure}) = 1 - P(\text{success}) = 1 - \frac{1}{4} = \frac{3}{4}$.

Answer:

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