Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them t

Question

2 months ago

7

Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them t

o catch up to 8 fish. Assume each catch is independent. Which of the following represents the probability of needing to catch 8 fish to get the first salmon

Mathematics

1 answer:

lawyer [12.5K] · Answer 1 · 2026-02-16T04:55:07+03:00

Answer:

The likelihood of needing to catch 8 fish to obtain the first salmon is

(0.8)⁷ * 0.2 or 4.2% (when rounded to two decimal places)

Correct statement and question:

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Step-by-step explanation:

1. Let's revisit the details given to accurately solve this query:

The probability of catching a salmon in this river is 20% or 1/5.

Each fishing license allows for the capture of 8 fish.

Each catch is an independent event.

2. What represents the probability of needing to catch 8 fish to retrieve the first salmon?

Recall that the probability for independent events is formulated as:

P(A) * P(B)

Given that the probability of catching a salmon is at 20%, the likelihood of NOT catching one is (100% - 20%) = 80%.

Converting percentages to decimals:

80% = 0.8 and 20% = 0.2

To determine the probability of catching 8 fish before the first salmon, we need to calculate the probability of 7 catches resulting in no salmon and the final 8th catch being a salmon, expressed as:

P = 0.8 * 0.8 * 0.8 * 0.8 * 0.8 * 0.8 * 0.8 * 0.2

P = (0.8)⁷ * 0.2

P = 0.2097152 * 0.2

P = 0.042 (when rounded to two decimal places)

P = 4.2%