To find the probability of selecting a small, red fish from the aquarium, we first need to determine the number of small, red fish and the total number of fish in the aquarium.
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Total number of small fish: There are 8 small fish in total.
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Number of small, red fish: Half of the small fish are red. Therefore, the number of small, red fish is: \[ \text{Number of small red fish} = \frac{1}{2} \times 8 = 4 \]
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Total number of fish in the aquarium: There are 6 large fish and 8 small fish, so the total number of fish is: \[ \text{Total fish} = 6 + 8 = 14 \]
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Probability of selecting a small, red fish: The probability \( P \) of selecting a small, red fish can be calculated using the formula: \[ P(\text{small red fish}) = \frac{\text{Number of small red fish}}{\text{Total number of fish}} = \frac{4}{14} \]
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Simplifying the fraction: We can simplify \( \frac{4}{14} \): \[ \frac{4}{14} = \frac{2}{7} \]
Thus, the probability that a randomly selected fish is a small, red fish is \( \frac{2}{7} \).
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