In a discrete probability distribution, the sum of all possibilities is always?
Question
In a discrete probability distribution, the sum of all possibilities is always?
Solution
In a discrete probability distribution, the sum of all probabilities is always equal to 1.
Here are the steps to understand why:
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A discrete probability distribution is a list of probabilities associated with each of its possible outcomes. This is often represented in the form of a probability mass function.
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The probabilities in a discrete probability distribution represent the likelihood of an event occurring. For example, if you were to roll a fair six-sided die, the probability of rolling a 1, 2, 3, 4, 5, or 6 would each be 1/6.
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Because these probabilities represent all possible outcomes, when you add them together, they must total 1. This is because 1 represents certainty: something will definitely happen.
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Therefore, in a discrete probability distribution, the sum of all probabilities is always equal to 1. This is a fundamental principle of probability theory.
Similar Questions
True or false: The sum of the probabilities of any list of mutually exclusive and exhaustive events do not always equal 1.True false question.TrueFalse
Sure! Imagine you have two dice, and you roll them. The probability distribution of the sum of the dice tells us how likely each possible sum is to occur. To understand this, let's think about all the possible outcomes when rolling two dice. Each die has six sides, numbered from 1 to 6. So, when we roll the first die, we can get any number from 1 to 6. Similarly, when we roll the second die, we can also get any number from 1 to 6. To find the sum of the dice, we add the numbers that come up on each die. For example, if the first die shows a 3 and the second die shows a 4, the sum would be 3 + 4 = 7. Now, let's see how likely each sum is to occur. There are 36 possible outcomes when rolling two dice because each die has 6 possible outcomes, and we multiply those together (6 x 6 = 36). To find the probability of each sum, we count how many outcomes result in that sum and divide it by the total number of possible outcomes (36). Here is the probability distribution of the sum of two dice: Sum of dice: Probability: 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36 For example, the probability of getting a sum of 7 is 6/36 because there are 6 outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) that result in a sum of 7 out of the 36 possible outcomes. So, the probability distribution of the sum of two dice tells us how likely each sum is to occur when rolling two dice.
Select all that applyWhich of the following are key properties of the discrete probability distribution?Multiple select question.The probabilities of success and failure remain the same from trial to trialThe probability of each value x is a value between 0 and 1, or, equivalently, 0 ≤ P(X = x) ≤ 1The number of successes within a specified time or space interval equals any integer between zero and infinityThe sum of the probabilities equals 1. In other words, ΣP(X = xi) = 1, where the sum extends over all values x of X
The mean of the discrete probability distribution is also called the
is one of the most useful principles of enumeration in combinationatorics and discrete probability.ans.
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