[Java for Android App Development] Zatta:
I took the liberty to make your project, attached what I made of it. I was wrong in the meaning of arg1 of the OnCheckChanged method, it is an ID after all:

package by.zatta.radioexample;

import android.os.Bundle;
import android.app.Activity;
import android.view.View;
import android.view.View.OnClickListener;
import android.widget.Button;
import android.widget.EditText;
import android.widget.RadioGroup;
import android.widget.RadioGroup.OnCheckedChangeListener;
import android.widget.TextView;

public class MainActivity extends Activity implements OnCheckedChangeListener, OnClickListener {

EditText mEtOne;
EditText mEtTwo;
EditText mEtThree;
RadioGroup mRgSelect;
Button mBtnButton;
TextView mTvOutput;

[MENTION=439709]override[/MENTION]
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_main);

mEtOne = (EditText) findViewById(R.id.editText1);
mEtTwo = (EditText) findViewById(R.id.editText2);
mEtThree = (EditText) findViewById(R.id.editText3);
mRgSelect = (RadioGroup) findViewById(R.id.radioGroup1);
mBtnButton = (Button) findViewById(R.id.button1);
mTvOutput = (TextView) findViewById(R.id.textView1);

mBtnButton.setOnClickListener(this);
mRgSelect.setOnCheckedChangeListener(this);

}

[MENTION=439709]override[/MENTION]
public void onClick(View v) {
if (v.getId() == R.id.button1){
int selectedRB = mRgSelect.getCheckedRadioButtonId();

if (mEtOne.getText().toString().equals("")) mEtOne.setText("0");
if (mEtTwo.getText().toString().equals("")) mEtTwo.setText("0");
if (mEtThree.getText().toString().equals("")) mEtThree.setText("0");

int iOne = Integer.valueOf(mEtOne.getText().toString());
int iTwo = Integer.valueOf(mEtTwo.getText().toString());
int iThree = Integer.valueOf(mEtThree.getText().toString());

switch (selectedRB){
case R.id.radio0:
mTvOutput.setText("Sum = " + Integer.toString(iOne+iTwo));
break;
case R.id.radio1:
mTvOutput.setText("Multiplied = " + Integer.toString(iOne * iTwo * iThree));
break;
}
}
}

[MENTION=439709]override[/MENTION]
public void onCheckedChanged(RadioGroup arg0, int arg1) {

switch (arg1){
case R.id.radio0:
mEtThree.setVisibility(View.GONE);
mTvOutput.setText("Radio 0 is ticked");
break;
case R.id.radio1:
mEtThree.setVisibility(View.VISIBLE);
mTvOutput.setText("Radio 1 is ticked");
break;

}

}

}

the xml:

<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:paddingBottom="@dimen/activity_vertical_margin"
android:paddingLeft="@dimen/activity_horizontal_margin"
android:paddingRight="@dimen/activity_horizontal_margin"
android:paddingTop="@dimen/activity_vertical_margin"
tools:context=".MainActivity" >

<EditText
android:id="@+id/editText1"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_centerHorizontal="true"
android:layout_alignParentTop="true"
android:layout_marginTop="20dp"
android:ems="10"
android:inputType="number" />

<EditText
android:id="@+id/editText2"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_centerHorizontal="true"
android:layout_below="@+id/editText1"
android:ems="10"
android:inputType="number" />

<EditText
android:id="@+id/editText3"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_below="@+id/editText2"
android:layout_centerHorizontal="true"
android:visibility="gone"
android:ems="10"
android:inputType="number" />

<RadioGroup
android:id="@+id/radioGroup1"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_centerHorizontal="true"
android:layout_centerVertical="true" >

<RadioButton
android:id="@+id/radio0"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:checked="true"
android:text="Sum" />

<RadioButton
android:id="@+id/radio1"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:text="Multiply" />
</RadioGroup>

<TextView
android:id="@+id/textView1"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_above="@+id/button1"
android:layout_centerHorizontal="true"
android:layout_marginBottom="30dp"
android:text="Result"
android:textAppearance="?android:attr/textAppearanceLarge" />

<Button
android:id="@+id/button1"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignParentBottom="true"
android:layout_centerHorizontal="true"
android:text="Click me!" />

</RelativeLayout>