Question

fill in the blanks so that the resulting statement is true. because p(e) + p(not e) = 1, then p(not e) = ____ and p(e) = ____. because p(e) + p(not e) = 1, then p(not e) = and p(e) =

Explanation:

Step1: Solve for P(not E)

Given the equation \( P(E) + P(\text{not } E) = 1 \), we can isolate \( P(\text{not } E) \) by subtracting \( P(E) \) from both sides of the equation.
So, \( P(\text{not } E) = 1 - P(E) \).

Step2: Solve for P(E)

Similarly, to isolate \( P(E) \), we subtract \( P(\text{not } E) \) from both sides of the equation \( P(E) + P(\text{not } E) = 1 \).
This gives us \( P(E) = 1 - P(\text{not } E) \).

Answer:

\( P(\text{not } E) = \boldsymbol{1 - P(E)} \) and \( P(E) = \boldsymbol{1 - P(\text{not } E)} \)