Question

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Explanation:

Identify the given values and target

We are given:

• Total number of fish: \(N = 60\)
• Number of goldfish: \(G = 22\)
• Two fish are pulled sequentially without replacement.
• Target: Find the probability that both fish pulled are goldfish, rounded to the nearest hundredth.

Calculate the probability of the first event

Using the Theoretical Probability knowledge point, the probability of pulling a goldfish on the first draw is:

$$ P(G_1) = \frac{22}{60} = \frac{11}{30} $$

Calculate the conditional probability of the second event

Using the Dependent Events and Conditional Probability knowledge points

$$ P(G_2 \mid G_1) = \frac{22 - 1}{60 - 1} = \frac{21}{59} $$

Calculate the joint probability of both events

Using the Dependent Events and Conditional Probability knowledge points

$$ P(G_1 \cap G_2) = P(G_1) \times P(G_2 \mid G_1) = \frac{22}{60} \times \frac{21}{59} = \frac{462}{3540} \approx 0.1305 $$

Round the final probability

Rounding \(0.1305\) to the nearest hundredth gives:

$$ P(\text{both goldfish}) \approx 0.13 $$

Answer:

0.13