\(P\)(The card is a king | The card is a face card) \(\neq\) \(P\)(The card is a king) Whenever the probability of an event \(E\) is not affected by the occurrence of another event \(F\), and vice ver...\(P\)(The card is a king | The card is a face card) \(\neq\) \(P\)(The card is a king) Whenever the probability of an event \(E\) is not affected by the occurrence of another event \(F\), and vice versa, we say that the two events \(E\) and \(F\) are independent. Both solutions to Example \(\PageIndex{8}\) are actually the same, except that in Solution 2 we delayed substituting the values into the equation until after we solved the equation for \(P(A \cap B)\).
\(P\)(The card is a king | The card is a face card) \(\neq\) \(P\)(The card is a king) Whenever the probability of an event \(E\) is not affected by the occurrence of another event \(F\), and vice ver...\(P\)(The card is a king | The card is a face card) \(\neq\) \(P\)(The card is a king) Whenever the probability of an event \(E\) is not affected by the occurrence of another event \(F\), and vice versa, we say that the two events \(E\) and \(F\) are independent. Both solutions to Example \(\PageIndex{8}\) are actually the same, except that in Solution 2 we delayed substituting the values into the equation until after we solved the equation for \(P(A \cap B)\).
