Confidence intervals in java, testing the random pick of an element in a list of objects

So I have this method that picks at random an object from a list of 2 objects. I would like to write a junit test (@Test) asserting based on a confidence level that somehow there's a 50% chance for each of the 2 objects to be picked.

The piece of code under test:

public MySepecialObj pickTheValue(List<MySepecialObj> objs, Random shufflingFactor) {

    // this could probably be done in a more efficient way
    // but my point is asserting on the 50% chance of the 
    // two objects inside the input list
    Collections.shuffle(objs, shufflingFactor);
    return objs.get(0);
}

In the test I would like to provide 2 mocks (firstMySepecialObjMock and secondMySepecialObjMock) as input objects of type MySepecialObj and new Random() as the input shuffling parameter, then assert that the firstMySepecialObjMock happens to be the choice 50% of the times and secondMySepecialObjMock happens to be the choice in the other 50% of the times.

Something like:

@Test
public void myTestShouldCheckTheConfidenceInterval() {

    // using Mockito here
    MySepecialObj firstMySepecialObjMock = mock(MySepecialObj.class);
    MySepecialObj secondMySepecialObjMock = mock(MySepecialObj.class);

    // using some helpers from Guava to build the input list
    List<MySepecialObj> theListOfTwoElements = Lists.newArrayList(firstMySepecialObjMock, secondMySepecialObjMock);

    // call the method (multiple times? how many?) like:
    MySepecialObj chosenValue = pickTheValue(theListOfTwoElements, new Random());

    // assert somehow on all the choices using a confidence level
    // verifying that firstMySepecialObjMock was picked ~50% of the times
    // and secondMySepecialObjMock was picked the other ~50% of the times
}

I am not sure about the statistics theory here, so maybe I should provide a different instance of Random with different parameters to its constructor?

I would also like to have a test where I could set the confidence level as a parameter (I guess usually is 95%, but it could be another value?).

• What could be a pure java solution/setup of the test involving a confidence level parameter?
• What could be an equivalent solution/setup of the test involving some helper library like the Apache Commons?