Question 1120628: 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, 2 will be tall and colorless, 3 will be short and colorful, and 2 will be short and colorless.
The probability is_______________
Answer by greenestamps(13198)   (Show Source):
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The number of ways of selecting 10 plants with 3 tall and colorful, 2 tall and colorless, 3 short and colorful, and 2 short and colorless is given by the multinomial coefficient
The probability of any one of those combinations is
The overall probability of selecting that number of the different kinds of plants is the product of those two numbers, which to a few decimal places is 0.00165.
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