Answer: C. 0.0180
Step-by-step explanation:
Let x be the binomial variable that represents the number of seeds will germinate with parameter
n= 30 (Number of trials)
p=0.90 (Probability of success in each event)
Binomial probability formula :
Probability of getting success in x trials : [tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]
For x= 23 , we have
[tex]P(X=23)=^{30}C_{23}(0.90)^{23}(0.10)^{7}\\\\=\dfrac{30!}{23!(30-23)!}(0.90)^{23}(0.10)^7[/tex]
Simplify
[tex]P(x=23)=0.018043169424\approx0.0180[/tex]
Hence, the probability that exactly 23 seeds will germinate = 0.0180
