Mathematics, 05.12.2019 04:31 devbar3416

Select all of the statements that are axioms of probability.

a) the probability of two events occurring is always greater than 0.

b) the probability of an event a is the number of outcomes in a divided by the number of outcomes in the sample space.

c) the probability of an event is a number that is at least 0 and no more than 1.

d) if two events a and b are mutually exclusive (disjoint), then p(a or b)=p(a)+p(b).

e) the combined probability of all possible outcomes is equal to 1.

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Answer from: brae72

We want to select the statements that are axioms of probability.

We will see that the correct options are C, D, and E.

The easier thing to do, is writing the axioms and see which statements relate to those.

The axioms of probability are:

The probability of an event is a non-negative real number and equal to or smaller than 1. The probability of one of all the possible events to happen is 1, this also means that the sum of all the probabilities of the individual events is equal to 1.The probability (assuming additivity) of one event or other happening is equal to the sum of the probabilities.

Now that we know the axioms, let's see if the statements relate to them or not.

A) The probability of two events occurring is always greater than 0.

false, if we take two events with a probability of zero, then the probability of these two events occurring is zero.

B) The probability of an event A is the number of outcomes in A divided by the number of outcomes in the sample space.

This is false, this is only true when all the outcomes in the sample space have the same probability of happening.

C) The probability of an event is a number that is at least 0 and no more than 1.

True, by the first axiom.

D) If two events A and B are mutually exclusive (disjoint), then P(A or B)=P(A)+P(B).

True, related to the third axiom, disjoint events are additive.

E) The combined probability of all possible outcomes is equal to 1.

True, by the second axiom.

so the correct options are C, D, and E.

If you want to learn more, you can read:

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Answer from: hollisjune3047

All options are true

Step-by-step explanation:

Probability of an event:it is defined as the possibility of an event is happening.

Mathematical representation:

$P(E)=\frac{Number\;of\;favorable\;cases}{Total\;number\;of cases}$

Probability of an event is always greater than or equal to 0 and less than 1 or equal to 1.

The sum of probabilities of all outcomes of an experiment is equal to 1.

When two events A and B are disjoint , then

$A\cap B=\phi$

$P(A\cap B)=0$

$P(A\cup B)=P(A)+P(B)-0=P(A)+P(B)$

P(E)+P(E')=1

Hence, all option are true.

Answer from: Quest

Xis -1/2
y is 35/4.
18x-9y=-18 12x+8y=64 what does x equal and what does y equal?

Answer from: Quest

where is the diagram? shown below where? ?

step-by-step explanation:

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Select all of the statements that are axioms of probability.

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