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

The probability of catching the first salmon out of 8 fish is 0.0419.

Given information:

Once a year, people can purchase a fishing license that allows them to catch up to 8 fish.

Each catch is independent. (independent events)

The probability of fishing a salmon in a certain river is 20 percent or 0.2.

Now, the probability of not getting a salmon will be 80% or 0.8.

So, the first fish should be salmon and the others should not be salmon. So, the required probability of independent events can be calculated as,

Therefore, the probability of catching the first salmon out of 8 fish is 0.0419.

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The probability of needing to catch 8 fish to get the first salmon is

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

Correct statement and question:

Options were not provided, we looked for them either at or other site, but we didn't find them. We will answer the problem without using any additional source, just the information provided.

Step-by-step explanation:

1. Let's review the information given to us to solve the question correctly:

Probability of fishing a salmon in a certain river = 20% or 1/5

Number of fishes allowed per fishing license = 8

Each catch is an independent event

2. Which of the following represents the probability of needing to catch 8 fish to get the first salmon?

Let's recall that the probability for independent events is:

P(A) * P(B)

Now, if the probability of fishing a salmon is 20%, the probability of NOT fishing a salmon is (100% - 20%) = 80%

Let's convert the percent to decimal.

80% = 0.8 and 20% = 0.2

If we need to catch 8 fishes to get the first salmon, we can find out the probability of 7 catches not fishing a salmon and the 8th, catching finally a salmon, this way:

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 (rounding to two decimal places)

P = 4.2%