Answered

Join IDNLearn.com today and start getting the answers you've been searching for. Our community is here to provide detailed and trustworthy answers to any questions you may have.

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 :

GinnyAnsweridn
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
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.