Question

suppose that the probability a seed will germinate is 80%. what is the probability that 7 of these seeds will germinate when 10 are planted?
a. 1.0068
b. 25.17
c. 120
d. 0.201
please select the best answer from the choices provided
○ a
○ b
○ c
○ d

Explanation:

Step1: Use binomial probability formula

Binomial probability formula is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n = 10\), \(k = 7\), \(p=0.8\), \(1-p = 0.2\)

Step2: Calculate combination \(C(n,k)\)

\(C(10,7)=\frac{10!}{7!(10 - 7)!}=\frac{10\times9\times8}{3\times2\times1}=120\)

Step3: Substitute values into formula

\(P(X = 7)=120\times(0.8)^{7}\times(0.2)^{3}\)
\(P(X = 7)=120\times0.2097152\times0.008\)
\(P(X = 7)\approx0.201\)

Answer:

D. 0.201