To determine the probability of Laila guessing correctly or incorrectly on a multiple-choice question with 4 answer choices, let's follow these steps:
1. Understand the probability of a correct guess (success):
- Since there are 4 answer choices and only one of them is correct, the probability of selecting the correct answer out of these 4 choices is [tex]\( \frac{1}{4} \)[/tex].
2. Understand the probability of an incorrect guess (failure):
- Conversely, the probability of selecting any of the 3 incorrect answers out of these 4 choices is [tex]\( \frac{3}{4} \)[/tex].
Now, let's match these probabilities with the choices provided:
- a) [tex]\( P(\text{success}) = \frac{1}{4}, P(\text{failure}) = \frac{3}{4} \)[/tex]
- b) [tex]\( P(\text{success}) = \frac{1}{4}, P(\text{failure}) = \frac{1}{2} \)[/tex]
- c) [tex]\( P(\text{success}) = \frac{3}{4}, P(\text{failure}) = \frac{1}{4} \)[/tex]
- d) [tex]\( P(\text{success}) = 1, P(\text{failure}) = 0 \)[/tex]
The correct answer, given the probabilities [tex]\( \frac{1}{4} \)[/tex] for a correct guess and [tex]\( \frac{3}{4} \)[/tex] for an incorrect guess, matches option (a).
Thus, the correct answer is:
[tex]\( \mathbf{a \; P(\text{success}) = \frac{1}{4}, \; P(\text{failure}) = \frac{3}{4}} \)[/tex].
