Which of the following are true for probability? CHECK ALL THAT APPLY! If P(A)=0
ID: 3075053 • Letter: W
Question
Which of the following are true for probability? CHECK ALL THAT APPLY!
If P(A)=0 for an event A, that means A cannot happen.
The total probability of all possible outcomes of an experiment adds up to 1.
P(A|B) = P(A) means that these two events are independent.
The probability is a value between -1 and 1.
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.
Explanation / Answer
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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