Which of the following are true for probability? CHECK ALL THAT APPLY! a) If P(A)=0 for...

Which of the following are true for probability? CHECK ALL THAT APPLY!

a)		If P(A)=0 for an event A, that means A cannot happen.
b)		The total probability of all possible outcomes of an experiment adds up to 1.
c)		P(A\|B) = P(A) means that these two events are independent.
d)		The probability is a value between -1 and 1.

Solutions

Expert Solution

Let us talk on each option one-by-one,

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Option a)

In the usual measure theoretic formulation of probability, ''event'' is a set of outcomes; an event is realized if the outcome of the experiment is within the set. Impossible event is the empty set ∅, i.e. under no outcome of the experiment can this event be realized.

Let X be a random variable with uniform distribution on [0,1] and A be the event X=0.5 (or any other real number on [0,1]. This is obviously not a null event (such random variate can take the value of 0.5 but has the probability of zero (as the distribution is continuous).

So, It is NOT TRUE for all cases.

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Option b)

The total probability of all possible outcomes of an experiment adds up to 1.

#This is an statndard axiom of probability.

So, It is TRUE.

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Option c)

If P(A|B) = P(A), then events A and B are said to be independent: in such a case, having knowledge about either event does not change our knowledge about the other event.

It is TRUE .

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Option d)

The probability is a value between 0 and 1.

It is NOT TRUE.

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orchestra answered 1 year ago

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