taiwan-gsat 2021 Q2

taiwan-gsat · Other · ast__math-a 6 marks Conditional Probability Conditional Probability as a Function of a Parameter
A research team uses a certain rapid test reagent to understand the proportion of organisms in a protected area whose body toxin accumulation exceeds the standard due to environmental pollution. The test result of this reagent shows only two colors: red and yellow. Based on past experience, it is known that: if body toxin accumulation exceeds the standard, after testing with this reagent, $75\%$ shows red; if body toxin accumulation does not exceed the standard, after testing with this reagent, $95\%$ shows yellow. It is known that for a certain type of organism in this protected area, $7.8\%$ of the test results show red. Assuming the actual proportion of this type of organism with body toxin accumulation exceeding the standard is $p\%$ , select the correct option.
(1) $1 \leq p < 3$
(2) $3 \leq p < 5$
(3) $5 \leq p < 7$
(4) $7 \leq p < 9$
(5) $9 \leq p < 11$
A research team uses a certain rapid test reagent to understand the proportion of organisms in a protected area whose body toxin accumulation exceeds the standard due to environmental pollution. The test result of this reagent shows only two colors: red and yellow.\\
Based on past experience, it is known that: if body toxin accumulation exceeds the standard, after testing with this reagent, $75\%$ shows red; if body toxin accumulation does not exceed the standard, after testing with this reagent, $95\%$ shows yellow. It is known that for a certain type of organism in this protected area, $7.8\%$ of the test results show red. Assuming the actual proportion of this type of organism with body toxin accumulation exceeding the standard is $p\%$ , select the correct option.\\
(1) $1 \leq p < 3$\\
(2) $3 \leq p < 5$\\
(3) $5 \leq p < 7$\\
(4) $7 \leq p < 9$\\
(5) $9 \leq p < 11$