When the earth wire is connected to the metal case of the washing machine, it provides an alternative pathway for electric current to flow if there is a fault, such as if the live wire touches the metal case. The earth wire is connected to the ground, which has zero potential, so any current that flows through the earth wire will not harm a person who touches the metal case. This is because the person's body is also at zero potential (ground potential) and there will be no potential difference (voltage) across the person's body, which means no electric current will flow through the person's body. Therefore, connecting the earth wire to the metal case of the washing machine ensures that any electrical faults will be safely conducted away from the person, reducing the risk of electric shock or electrocution.