This month Carla caught the following fish in Lake George, 24 trout, 41 sunfish, 12 perch and 23 blue gills. If Carla catches another fish this month, what is the probability of her catching a trout? A. about 1/2 B. about 1/4 C. about 1/24 D. about 1 My answer is I think 1/24 is this correct?
The correct answer and explanation is:
Your answer of 1/24 is not correct. Let’s work through the correct solution together and then explain it clearly.
Step-by-Step Solution:
Carla caught the following fish this month:
- Trout: 24
- Sunfish: 41
- Perch: 12
- Blue gills: 23
Total fish caught so far:
24 (trout) + 41 (sunfish) + 12 (perch) + 23 (blue gills) = 100 fish
If she catches one more fish, and assuming the chances of catching each type are proportional to the numbers caught so far, we want the probability that this fish is a trout.
So, the probability of catching a trout is: Number of troutTotal number of fish=24100=625\frac{\text{Number of trout}}{\text{Total number of fish}} = \frac{24}{100} = \frac{6}{25}
Now let’s approximate 625\frac{6}{25}: 625=0.24≈14\frac{6}{25} = 0.24 \approx \frac{1}{4}
Correct Answer: B. about 1/4
Explanation (300 words):
Probability is the measure of how likely an event is to occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this problem, we are given how many of each type of fish Carla has caught in Lake George this month. Specifically, she caught 24 trout, 41 sunfish, 12 perch, and 23 blue gills. The total number of fish she has caught is 100.
If we assume that her future catches will follow the same pattern as her past catches — meaning the probability of catching any particular type of fish is proportional to how many of that type she has already caught — then we can use the existing data to estimate the chances of catching another trout.
Out of 100 fish, 24 were trout. Therefore, the chance of catching another trout is 24 out of 100, or 24%. This fraction simplifies to 625\frac{6}{25}, which is approximately 0.24. Since 0.24 is close to 0.25, and 14=0.25\frac{1}{4} = 0.25, we can say that the probability of catching a trout is about 14\frac{1}{4}.
The option you chose, 1/24, would suggest only a 4.17% chance of catching a trout, which is much too low. That might come from misinterpreting the 24 trout as out of a larger total, like 576, which is not the case here.
So, the correct answer is B. about 1/4.