According to a theory in genetics, if tall and colorful plants are crossed with short and colorless plants, four types of plants will result: tall and colorful, tall and colorless, short and colorful, and short and colorless, with corresponding probabilities of nine sixteenths , three sixteenths , three sixteenths , and one sixteenth . In a multinomial experiment, if 10 plants are selected, find 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.

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

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.