If x is a discrete uniform random variable ranging from 0 to 12, find p(x ≥ 10).

Solution:

The set of uniform random variables range from 0 10 12 which means that the population size is N = 13.

The problem statement is about choosing or selecting a number as a variable from the population.

So any of the following 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 can be chosen in a random manner.

As per the problem statement it is to be determined that if a number is randomly selected then what is the probability that it will be greater than equal to 10.

Numbers which are equal and greater than 10 are 10, 11, and 12 i.e. desired outcomes are three in number.

The total number of outcomes possible is 13. Therefore

P(x ≥ 10) = Total Number of desired outcome / Total Number of outcomes = 3/13

There is another approach to solve this problem.

We can state that we have to find the probability P(10 or 11 or 13) i.e. the probability that the selected variable is either 10, 11, or 12.

Mathematically this can be stated as the universal addition principle:

P(10 or 11 or 12) = P(10) + P(11) + P(12) - P(10 & 11 & 12) --- (1)

= 1/13 + 1/13 + 1/13 - 0

= 3/13

The last term in equation (1) i.e. P(10 & 11 & 12) is zero because only one number can be selected at a time.

In other words the events are mutually exclusive events i.e. events of 10, 11 or 12 cannot occur together.

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If x is a discrete uniform random variable ranging from 0 to 12, find p(x ≥ 10).

Summary:

If x is a discrete uniform random variable ranging from 0 to 12, then the probability p(x ≥ 10) is 3/13.