SOLUTION: When 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 a

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Question 1100100: When 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: 0.37, 0.42, 0.11, and 0.10. Ten plants are selected.
Find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless.
Answer by greenestamps(13196) About Me  (Show Source):
You can put this solution on YOUR website!

Denoting the four types of plants as A, B, C, and D, the "probability vector" for each plant is

0.37A%2B0.42B%2B0.11C%2B0.10D

The probability of selecting 10 plants and getting 5 of A, 2 each of B and C, and 1 of D, is given by the coefficient of the %28A%5E5%29%28B%5E2%29%28C%5E2%29%28D%5E1%29 term in the expansion of %280.37A%2B0.42B%2B0.11C%2B0.10D%29%5E10

While the actual computation is ugly, the multinomial formula gives us the required calculation:



I'll let you crunch the numbers....