# 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.

Last updated date: 23rd Mar 2023

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Answer

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Hint- Identical balls mean that it doesn’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 doesn’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.

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 doesn’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.

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