Given:
If a seed is planted, it has a 80% chance of growing into a healthy plant.
10 seeds are planted.
Required:
To find the probability that exactly 3 don't grow.
Explanation:
[tex]\begin{gathered} p=80\% \\ \\ =0.8 \\ \\ 1-p=1-0.8 \\ \\ =0.2 \end{gathered}[/tex][tex]\begin{gathered} N=10 \\ k=3 \end{gathered}[/tex]
Seven success in 10 trails, therefore
[tex]\begin{gathered} =(10\text{ choose 7\rparen}\times(0.8)^7\times(0.2)^3 \\ \\ =\frac{(10\times9\times8)}{(3\times2)}\times(0.8)^7\times(0.2)^3 \\ \\ =(5\times3\times8)\times0.2097\times0.008 \end{gathered}[/tex][tex]=0.2013[/tex]
Therefore 20% that exactly 3 don't grow.
Final Answer:
[tex]20\%[/tex]
