Question

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 five sixteenths ​, four sixteenths ​, one sixteenth ​, and six sixteenths . 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, 1 will be short and​ colorful, and 3 will be short and colorless.

Please write out the formula, thanks!

Answer 1

Ans:

For multi-nomial distribution:

P = [ n! / ( n₁! * n₂! * ... n_k! ) ] * ( p₁^n₁ * p₂^n₂ * . . . * p_k^n_k )

P(x₁=3,x₂=3,x₃=1,x₄=3)

=10!/(3!*3!*1!*3!)*((5/16)^3*(4/16)^3*(1/16)*(6/16)^3)

=0.0264