The correct answer and explanation is:
The correct answer is 6/25.
To find the probability of Carla catching a trout, we must first determine the total number of fish she has caught this month. This total represents all the possible outcomes for her next catch. The problem provides the following numbers for each type of fish:
- Trout: 24
- Sunfish: 41
- Perch: 12
- Blue gills: 23
We can calculate the total number of fish by adding these individual counts together:
Total fish = 24 + 41 + 12 + 23 = 100
So, Carla has caught a total of 100 fish. This number will be the denominator in our probability fraction, as it represents the total size of the sample space.
Next, we need to identify the number of “favorable outcomes.” In this case, a favorable outcome is catching a trout. The problem states that Carla caught 24 trout. This number will be the numerator of our probability fraction.
The formula for probability is:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Using the numbers we have identified:
Probability of catching a trout = 24 / 100
This fraction, 24/100, correctly represents the probability. However, it is standard practice to simplify fractions to their lowest terms. To do this, we find the greatest common divisor for both the numerator (24) and the denominator (100). The largest number that divides evenly into both 24 and 100 is 4.
We divide both parts of the fraction by 4:
24 ÷ 4 = 6
100 ÷ 4 = 25
This gives us the simplified fraction 6/25. Therefore, the probability that Carla’s next catch will be a trout is 6 out of 25. This can also be expressed as a decimal (0.24) or a percentage (24 percent).
