Answer:
The probability that 3 will be tall and colorful, 3 will be tall and colorless, 3 will be short and colorful, and 1 will be short and colorless out of 10 plants is 0.0081.
Step-by-step explanation:
As the values of different probabilities are given as
X1=tall and colorful, P(X1)=9/16
X2=tall and colorless, P(X2)=3/16
X3=short and colorful, P(X3)=3/16
X4=short and colorless, P(X4)=1/16
Now the total number of plants is 10 and the X1=3, X2=3,X3=3,X4=1
so
![P(X1=n_1,X2=n_2,X3=n_3,X4=n_4)=\dfrac{n!}{n_1!n_2!n_3!n_4!}p_1^{n_1}p_2^{n_2}p_3^{n_3}p_4^{n_4}\\=\dfrac{10!}{3!3!3!1!}\left(\dfrac{9}{16}\right)^{3}\left(\dfrac{3}{16}\right)^{3}\left(\dfrac{3}{16}\right)^{3}\left(\dfrac{1}{16}\right)^{1}\\=\dfrac{279006525}{2^{33}\cdot \:4}\\=0.0081](https://tex.z-dn.net/?f=P%28X1%3Dn_1%2CX2%3Dn_2%2CX3%3Dn_3%2CX4%3Dn_4%29%3D%5Cdfrac%7Bn%21%7D%7Bn_1%21n_2%21n_3%21n_4%21%7Dp_1%5E%7Bn_1%7Dp_2%5E%7Bn_2%7Dp_3%5E%7Bn_3%7Dp_4%5E%7Bn_4%7D%5C%5C%3D%5Cdfrac%7B10%21%7D%7B3%213%213%211%21%7D%5Cleft%28%5Cdfrac%7B9%7D%7B16%7D%5Cright%29%5E%7B3%7D%5Cleft%28%5Cdfrac%7B3%7D%7B16%7D%5Cright%29%5E%7B3%7D%5Cleft%28%5Cdfrac%7B3%7D%7B16%7D%5Cright%29%5E%7B3%7D%5Cleft%28%5Cdfrac%7B1%7D%7B16%7D%5Cright%29%5E%7B1%7D%5C%5C%3D%5Cdfrac%7B279006525%7D%7B2%5E%7B33%7D%5Ccdot%20%5C%3A4%7D%5C%5C%3D0.0081)
So the probability that 3 will be tall and colorful, 3 will be tall and colorless, 3 will be short and colorful, and 1 will be short and colorless out of 10 plants is 0.0081.