Probability of distribution of two random variables

From probability... Distributions of two random variables. The Correlation Coefficient.

1. A certain species of plant produces a flower that is either red, pink, white or on rare occasions blue. Form an analysis of the plants genes it is possible to calculate the the probability of a red flower is , the probability of white is and the probability of a pink flower is . A gardener grow 20 of these plants and was pleasantly suprised to see 5 blue flowers, 10 red, 2 white and 2 pink. Calculated the probability of this event.

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Solution. First of all, we can assume that the events that each plant will produce a blue flower, a red flower, a white flower, or a pink flower are independent.

Secondly, we need to find the number of ways that we partition these 20 plants into FOUR groups: the 1st group has 5 plants; the 2nd group has 10 plants; the 3rd group has 3 plants; and the 4th group has 2 plants. The total number of ways is equal to

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The probability of an event is found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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