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) 0.20 0.16 0.28 0.24
Would it be 0.11??
To determine the number of green elements required to make this a legitimate probability distribution, we need to ensure that the sum of all probabilities is equal to 1.
Given the probabilities for each color:
P(red) = 0.20
P(blue) = 0.16
P(orange) = 0.28
P(brown) = 0.24
We can calculate the sum of these probabilities:
0.20 + 0.16 + 0.28 + 0.24 = 0.88
To make this a legitimate probability distribution, the sum of all probabilities should be equal to 1. However, the sum of the given probabilities is 0.88, which means we need to determine the probability of the green elements (P(green)) in order to complete the distribution.
To calculate the probability of the green elements (P(green)), we can subtract the sum of the given probabilities (0.88) from 1:
1 - 0.88 = 0.12
Therefore, the probability of the green elements is 0.12.
To determine the number of green elements required, we need to multiply the probability (P(green)) by the total number of elements in the sample (50):
0.12 * 50 = 6
Hence, 6 green elements are required to make this a legitimate probability distribution.