How many green elements are required to make this a legitimate probability distribution if there are a total of 50 elements in this sample?
x red blue orange brown green
P(x) 0.18 0.20 0.32 0.28
To make this a legitimate probability distribution, the sum of all probabilities should be equal to 1. In other words, the sum of the probabilities for all elements should add up to 1.
In this case, the sum of the probabilities given for red, blue, orange, brown, and green should be equal to 1.
Let's calculate the sum of the given probabilities:
Sum = 0.18 + 0.20 + 0.32 + 0.28 + P(green)
We are given that the sum should be equal to 1, so we can set up the equation:
0.18 + 0.20 + 0.32 + 0.28 + P(green) = 1
Now, rearranging the equation, we get:
P(green) = 1 - (0.18 + 0.20 + 0.32 + 0.28)
P(green) = 1 - 0.98
P(green) = 0.02
Therefore, the probability of getting a green element in this sample is 0.02.
To calculate the number of green elements, we need to know the total number of elements in the sample. In this case, there are 50 elements.
If we assume that the given probabilities represent the relative frequencies of each color, we can calculate the number of green elements by multiplying the probability of getting a green element (0.02) by the total number of elements (50).
Number of green elements = P(green) * Total elements
Number of green elements = 0.02 * 50
Number of green elements = 1
So, to make this a legitimate probability distribution with a total of 50 elements, you would need 1 green element.