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Let [tex]\( A \)[/tex] be an event within the sample space [tex]\( S \)[/tex], and let [tex]\( n(A) = a \)[/tex] and [tex]\( n(S) \)[/tex].

Choose the correct expression below:

A. [tex]\( 2P\left(A^{\prime}\right) \)[/tex]
B. 0
C. [tex]\( { }^{2P}(A) \)[/tex]
D. 1
E. [tex]\( 1 - P\left(A^{\prime}\right) \)[/tex]
F. [tex]\( 1 - P(A) \)[/tex]



Answer :

GinnyAnswer
To solve this problem, we need to understand the relationship between the probabilities of an event and its complement.

Let's denote the probability of event [tex]\( A \)[/tex] as [tex]\( P(A) \)[/tex]. The probability of the complement of [tex]\( A \)[/tex], denoted as [tex]\( A' \)[/tex], is given by:

[tex]\[ P(A') = 1 - P(A) \][/tex]

The question asks to find the correct expression related to the probability of event [tex]\( A \)[/tex].

Given that:

[tex]\[ P(A) = 0.5 \][/tex]

We want to find the value of [tex]\( 1 - P(A) \)[/tex]. By substituting [tex]\( P(A) \)[/tex] with 0.5:

[tex]\[ P(A') = 1 - P(A) = 1 - 0.5 = 0.5 \][/tex]

So, the correct expression for [tex]\( 1 - P(A) \)[/tex] is:

[tex]\[ 1 - P(A) \][/tex]

Among the options provided, the one that matches this expression is:

F. [tex]\( 1 - P(A) \)[/tex]

Therefore, the correct answer is:

F. [tex]\( 1 - P(A) \)[/tex]

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