Question

a pond contains only three different types of fish. olivia caught a fish from the pond, recorded its type and then returned it back to the pond. she did this a total of 10 times. the table below shows some of her results.

a) how many times did she catch a trout?

b) olivia catches another fish from the pond. which type of fish is it most likely to be?

type of fish	number caught	relative frequency
pike	3
trout

Explanation:

🆕 New Concept Discovered: Relative Frequency and Probability
Using experimental data to estimate likelihoods

Step 1: Find the number of Sunfish caught

The relative frequency of Sunfish is \( 0.5 \). Relative frequency represents the proportion of the total trials in which an event occurs:

$$ \text{Relative frequency} = \frac{\text{Number of times caught}}{\text{Total trials}} $$

Given the total number of trials is \( 10 \):

$$ 0.5 = \frac{\text{Number of Sunfish}}{10} $$

$$ \text{Number of Sunfish} = 0.5 \times 10 = 5 $$

Step 2: Calculate the number of Trout caught

The total number of fish caught is \( 10 \). The pond contains only Sunfish, Pike, and Trout.

$$ \text{Sunfish} + \text{Pike} + \text{Trout} = 10 $$

$$ 5 + 3 + \text{Trout} = 10 $$

$$ 8 + \text{Trout} = 10 $$

$$ \text{Trout} = 10 - 8 = 2 $$

So, Olivia caught a Trout \( 2 \) times.

Step 3: Determine the most likely type of fish

To find which fish is most likely to be caught next, we compare the number of times each fish was caught (or their relative frequencies):

• Sunfish: \( 5 \) times (Relative frequency = \( 0.5 \))
• Pike: \( 3 \) times (Relative frequency = \( \frac{3}{10} = 0.3 \))
• Trout: \( 2 \) times (Relative frequency = \( \frac{2}{10} = 0.2 \))

Since Sunfish has the highest frequency and relative frequency, it is the most likely type of fish to be caught next.

Answer:

a) 2

b) Sunfish