A bag contains the two tiles shown. One tile is drawn at random from the bag. The tile is returned to the bag and again a tile is drawn from the bag.


What is the sample space for this experiment?



A.
{L, M}

B.
{LL, LM, MM}

C.
{LL, LM, ML, MM}

D.
{L}

{L,M} is the Ω (sample space) for one single draw.

When there are two draws one after another with replacement, the sample space will contain
LL
LM
ML
MM

To determine the sample space for this experiment, we need to consider all possible outcomes or combinations of tiles that can be drawn from the bag.

In this scenario, there are two tiles: "L" and "M". When we draw a tile from the bag and replace it, there are two possible outcomes - either we draw an "L" or an "M".

So the first draw can result in either "L" or "M". And when we draw the second time, regardless of what was drawn initially, there can again be two possible outcomes - either "L" or "M".

To find the sample space, we consider all possible combinations of the first and second draws.

The sample space is the set of all possible outcomes, which in this case would be:

{LL, LM, ML, MM}

Therefore, the correct answer is option C. {LL, LM, ML, MM}.

A{L,M}