Answered

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Given:
- Event A and Event B are mutually exclusive.
- Event A and Event C are not mutually exclusive.
- [tex]\(P(A) = 0.45\)[/tex]
- [tex]\(P(B) = 0.35\)[/tex]
- [tex]\(P(C) = 0.25\)[/tex]

What is the probability of the complement of Event A?

A. 1.00
B. 0.10
C. 0.45
D. 0.55

Sagot :

GinnyAnswer
To find the probability of the complement of Event [tex]\( A \)[/tex], we use the fundamental rule of complements in probability. The rule states that the probability of the complement of an event [tex]\( A \)[/tex], denoted as [tex]\( P(A^c) \)[/tex], is equal to one minus the probability of the event [tex]\( A \)[/tex]. Mathematically, this is expressed as:

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

Given that [tex]\( P(A) = 0.45 \)[/tex], we substitute this value into the formula:

[tex]\[ P(A^c) = 1 - 0.45 \][/tex]

When we perform the subtraction, we get:

[tex]\[ P(A^c) = 0.55 \][/tex]

So, the probability of the complement of Event [tex]\( A \)[/tex] is [tex]\( 0.55 \)[/tex].

Therefore, the correct answer is:

0.55
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