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

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(13198) (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

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 term in the expansion of

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

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