The probability of event A is $P\left(A\right)=0.05$P(A)=0.05​ . Find the probability of the complement of event A.$P\left(\overline{A}\right)=$P(A)=​

1. Break Down the Problem

We need to find the probability of the complement of event A, denoted as $P(\overline{A})$. The complement rule states that the probability of event A not occurring is equal to 1 minus the probability of event A occurring.

2. Relevant Concepts

The formula for the probability of the complement event is: $P(\overline{A}) = 1 - P(A)$

3. Analysis and Detail

We know that: $P(A) = 0.05$ Now applying the complement rule: $P(\overline{A}) = 1 - P(A) = 1 - 0.05$

4. Verify and Summarize

Doing the calculation: $P(\overline{A}) = 1 - 0.05 = 0.95$ Thus, the complement of event A occurring has a probability of 0.95.

Final Answer

$P(\overline{A}) = 0.95$