If $P(E)=0.60, P\left(E\right.$ or $\left.F_{s}\right)=0.70$, and $P(E$ and $F)=0.05$, find $P(F)$.
$P(F)=\square$ (Simplify your answer.)
Answer
So, the probability of event F is \(\boxed{0.15}\).
Step 1 ：We are given that the probability of event E, denoted as \(P(E)\), is 0.60, the probability of either event E or event F occurring, denoted as \(P(E \cup F)\), is 0.70, and the probability of both events E and F occurring, denoted as \(P(E \cap F)\), is 0.05.
Step 2 ：We can find the probability of event F, denoted as \(P(F)\), using the formula \(P(F) = P(E \cup F) - P(E) + P(E \cap F)\).
Step 3 ：Substituting the given values into the formula, we get \(P(F) = 0.70 - 0.60 + 0.05\).
Step 4 ：Solving the equation gives us \(P(F) = 0.15\).
Step 5 ：So, the probability of event F is \(\boxed{0.15}\).
