how many green elements are required to make a legitimate probability distribution if there is a total of 50 elements in this sample?

x red blue orange brown green
p(x) 0.10 0.10 0.10 0.20 ?

* i am not sure but i don't think that any green elements are required but i am not sure if this is correct? please clarify and show work. thank you.

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To determine the number of green elements required to make a legitimate probability distribution, we need to remember that the sum of the probabilities for all possible outcomes in a probability distribution should equal 1. In this case, we are given that there are a total of 50 elements in the sample.

Let's first find the remaining probability for the green element. Since the sum of the probabilities for all the other elements is 0.10 + 0.10 + 0.10 + 0.20 = 0.50, the remaining probability for the green element can be calculated by subtracting 0.50 from 1:

1 - 0.50 = 0.50

Therefore, the remaining probability for the green element is 0.50.

To find the number of green elements required, we need to determine what portion of the sample they represent. Since we know that the total number of elements in the sample is 50 and the remaining probability for the green element is 0.50, we can calculate the number of green elements using the following equation:

(Number of green elements / Total number of elements) = Remaining probability for green element

Number of green elements / 50 = 0.50

To solve for the number of green elements, we can multiply both sides of the equation by 50:

Number of green elements = 50 * 0.50

Number of green elements = 25

So, in order to have a legitimate probability distribution with a total of 50 elements, you would need 25 green elements.