If \( P(E)=0.60, P(E \) or \( F)=0.80 \), and \( P(E \) and \( F)=0.10 \), find \( P(F) \). \( P(F)=\square \) (Simplify your answer.)

To find \( P(F) \), we can use the principle of inclusion-exclusion. The formula for the probability of the union of two events \( E \) and \( F \) is: \[ P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F) \] From the problem, we know: - \( P(E) = 0.60 \) - \( P(E \text{ or } F) = 0.80 \) - \( P(E \text{ and } F) = 0.10 \) Substituting the known values into the equation: \[ 0.80 = 0.60 + P(F) - 0.10 \] Now, simplify the equation: \[ 0.80 = 0.50 + P(F) \] Subtract \( 0.50 \) from both sides: \[ P(F) = 0.80 - 0.50 \] \[ P(F) = 0.30 \] Thus, the probability \( P(F) \) is: \[ P(F) = 0.30 \]