Question

A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Hint- Identical balls mean that it doesnâ€™t matter which white ball is drawn.

We have been given that number of
Red balls${\text{ = 1}}$
White balls${\text{ = 3}}$
Also we have been given that the white balls are identical. So, it doesnâ€™t matter which white ball is
drawn.
Now, two balls are drawn at random in succession without replacement,
So,
Let the red ball be $R$
Let the white ball be $W$
So making all possible options we get
${\text{Sample space = }}\left\{ {RW,{\text{ }}WW,{\text{ }}WR} \right\}$
Hence Sample Space${\text{ = 3}}$.

Note- In these types of questions we try all possible combinations and remembering that order does
matter here. That is (a, b) is not equal to (b, a). We must also remember that the white balls are
identical while solving the problem. Otherwise, we can also solve the question using combinations.