Question

A lake has 20 blue male, 30 red male, 60 blue female and 80 red female fish. A researcher catches one individual at random from the lake. If the caught fish is blue, the probability that it is female is ____________. (Rounded off to two decimal places)

Hint:

When a response occurs only in sympatry (where species co-occur) but not in allopatry, suspect \textbf{learning/experience}. If it appears everywhere, think \textbf{innate}.

Answer 1

Correct Answer: 0.74

Step 1 (Interpretation).
We need \(P(\text{female}\mid \text{blue})\). Use conditional probability: \[ P(F\mid B)=\frac{P(F\cap B)}{P(B)}=\frac{\#(F\cap B)}{\#(B)}. \]

Step 2 (Count the relevant categories only).
Blue total: \(\#(B)=\text{blue males}+\text{blue females}=20+60=80\).
Blue females: \(\#(F\cap B)=60\).

Step 3 (Compute).
\[ P(F\mid B)=\frac{60}{80}=\frac{3}{4}=0.75. \] Rounded to two decimals \Rightarrow \(\boxed{0.75}\).