The Correct Answer and Explanation is:
Of course. The correct answer is 20/67.
Here is a detailed explanation:
To solve this problem, we need to determine the probability of a specific event occurring. The fundamental formula for probability is:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
In this scenario, the “event” is Colin catching a trout on his next attempt. Let’s break down the problem into two parts based on the formula.
First, we need to identify the “number of favorable outcomes.” The question asks for the probability of catching a trout. According to the information provided, Colin has caught 20 trout. Therefore, the number of favorable outcomes is 20.
Second, we must calculate the “total number of possible outcomes.” This represents the total number of fish Colin has caught so far, as this data set is used to predict the likelihood of his next catch. We can find this by adding the quantities of all the different types of fish he has caught:
- Number of trout = 20
- Number of sunfish = 12
- Number of perch = 12
- Number of blue gills = 23
Total number of fish = 20 + 12 + 12 + 23 = 67
So, there are 67 total possible outcomes, as any of these fish could theoretically be the next one caught, based on the established catch rates.
Finally, we apply the probability formula by dividing the number of favorable outcomes (catching a trout) by the total number of possible outcomes (the total number of fish).
Probability of catching a trout = 20 / 67
This fraction cannot be simplified further. As a decimal, it is approximately 0.2985, which translates to about 29.85%. The most precise answer, however, is the fraction 20/67.
