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%
