Jimmy has to choose a coat and hat to wear outside. He has a choice of a red (R) or green (G) coat, and a choice of a blue (B) or yellow (Y) hat. What is the sample space for Jimmy's possible winter gear?

{GB, GY, RY, RB}

Step-by-step explanation:

Given : Jimmy has to choose a coat and hat to wear outside. He has a choice of a red (R) or green (G) coat, and a choice of a blue (B) or yellow (Y) hat.

To Find: What is the sample space for Jimmy's possible winter gear?

Solution:

Sample space : In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

To Form sample space

If he choose red coat (R) So, with that coat he can wear blue (B) or yellow (Y) hat.

So, sample space with red coat becomes {RY, RB}

Now If he choose green (G) coat So, with that coat he can wear blue (B) or yellow (Y) hat.

So, sample space with green coat becomes {GB, GY}

So, the sample space for the given situation is {GB, GY, RY, RB}

Hence the sample space for Jimmy's possible winter gear is {GB, GY, RY, RB}