This month, Carla caught the following fish in Lake George: trout, sunfish, perch, and blue gills. If Carla catches another fish this month, what is the probability of her catching a trout?
A. 24
B. 41
C. 12
D. 23
The correct answer and explanation is :
The question asks for the probability of Carla catching a trout on her next catch in Lake George, based on the information that she has already caught trout, sunfish, perch, and bluegills. To determine the probability, we must first calculate the total number of different types of fish Carla has caught and the number of trout.
Step 1: Identify the total number of different types of fish.
- Carla has caught four different types of fish this month: trout, sunfish, perch, and bluegills.
- So, the total number of types of fish Carla has caught is 4.
Step 2: Identify the number of trout Carla has caught.
- Since the question asks about the probability of catching a trout, it’s important to note that Carla has already caught one trout.
Step 3: Understand the concept of probability.
- Probability is defined as the ratio of favorable outcomes to the total possible outcomes. In this case, the favorable outcome is catching a trout, and the total possible outcomes are the different types of fish Carla could catch. $$
\text{Probability of catching a trout} = \frac{\text{Number of trout caught}}{\text{Total number of fish caught}}
$$
Step 4: Calculate the probability.
- Since Carla has caught one trout and four different types of fish, the probability of catching a trout on her next catch is: $$
\text{Probability of catching a trout} = \frac{1}{4}
$$
Step 5: Interpret the result.
- The probability of Carla catching a trout is 1/4 or 0.25, which corresponds to 25% of the possible outcomes.
Looking at the answer choices provided:
- A. 24
- B. 41
- C. 12
- D. 23
None of these options directly express the fraction 1/4 (which equals 25%). The correct probability should be 1/4 or 0.25, but the options given don’t match exactly. This suggests there may be a typographical error in the answer choices. Based on the calculation, the correct answer should be 1/4, though none of the options provided reflect this.