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Sagot :
Step 1: Concept
Use the binomial distribution to find the probability that exactly 11 of the chosen fish are yellow perch.
[tex]\begin{gathered} ^nC_rp^rq^{n-r} \\ p\text{ = probability that it is a yellow perch} \\ q\text{ = probability that it is not a yellow perch} \end{gathered}[/tex]Step 2:
Total = 18
Yellow perch = 13
Others = 5
Step 3:
[tex]\begin{gathered} p\text{ = }\frac{13}{18} \\ q\text{ = }\frac{5}{18} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} ^{15}C_{11}\text{ (}\frac{13}{18})^{11}(\frac{5}{18})^4 \\ =\text{ 1365 }\times\text{ 0.027885556 }\times\text{ 0.001653817169} \\ =\text{ }0.2266 \end{gathered}[/tex]Step 5: Final answer
The probability that exactly 11 of the chosen fish are yellow perch = 0.2266
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