The probability of one element is two times higher than the other. What are their probabilities?

Let's denote the probabilities of the two elements as P(A) and P(B). According to the given information, the probability of one element is two times higher than the other. This can be represented as:

P(A) = 2 * P(B)

Since the total probability of all outcomes must equal 1, we have:

P(A) + P(B) = 1

Substitute the first equation into the second equation:

2 * P(B) + P(B) = 1
3 * P(B) = 1
P(B) = 1/3

Now, substitute the value of P(B) back into the first equation to find P(A):

P(A) = 2 * (1/3) = 2/3

Therefore, the probabilities of the two elements are P(A) = 2/3 and P(B) = 1/3.

Let's represent the probabilities of the two elements as x and y.

Given that the probability of one element is two times higher than the other, we have:

x = 2y

The sum of probabilities of all elements in a sample space is always equal to 1. Therefore, we have:

x + y = 1

Substituting x = 2y into the second equation, we get:

2y + y = 1
3y = 1
y = 1/3

Therefore, x = 2y = 2(1/3) = 2/3.

Hence, the probabilities of the two elements are 2/3 and 1/3.