Which of the following probability values would complete the following probability distribution? P (x) 0 1/8 1 3/8 3 2 k 1/4
To find the missing value in the probability distribution, we can use the fact that the sum of all probabilities in a probability distribution must equal 1.
Given:
P(x) = 0, 1/8, 1, 3/8, 3, 2, k, 1/4
To find the missing value, we need to add up all the known probabilities and subtract the sum from 1:
0 + 1/8 + 1 + 3/8 + 3 + 2 + k + 1/4 = 1
Simplifying the equation, we have:
19/8 + k = 1 - (0 + 1/8 + 1 + 3/8 + 3 + 2 + 1/4)
19/8 + k = 1 - (27/8 + 3 + 2 + 1/4)
19/8 + k = 1 - (27/8 + 23/4)
19/8 + k = 1 - (27/8 + 46/8)
19/8 + k = 1 - 73/8
19/8 + k = -72/8
To solve for k, we can subtract 19/8 from both sides of the equation:
k = -72/8 - 19/8
k = -91/8
Therefore, the missing probability value in the distribution is -91/8.
To find the missing probability value (k) that would complete the probability distribution, we should start by summing up all the known probability values to see if they add up to 1. In a probability distribution, the total probability must always be equal to 1.
Given the known probabilities:
P(0) = 0
P(1) = 1/8
P(2) = 1/8
P(3) = 3/8
The sum of these probabilities is:
0 + 1/8 + 1/8 + 3/8 = 5/8
Since the sum of the known probabilities is not equal to 1, it means there is a missing probability value (k) that needs to be determined.
To find k, we need to subtract the sum of the known probabilities from 1:
k + 5/8 = 1
To solve for k, we subtract 5/8 from both sides:
k = 1 - 5/8
k = 8/8 - 5/8
k = 3/8
Therefore, the missing probability value (k) to complete the probability distribution is 3/8.