# A bag contains ﬁfteen balls distinguishable only by their colours; ten are blue and ﬁve are red. I reach into the bag with both hands and pull out two balls (one with each hand) and record their colours. What is the random phenomenon?, and What is the sample space?

Random phenomenon is the process of selecting two balls from a bag of different colored balls with unknown composition. It is an example of a discrete random variable, which can be described as a set of outcomes that can each occur with some probability.

The sample space for this experiment consists of all the possible combinations of two balls taken from the bag. This includes both the 10 blue and 5 red balls in any order, giving us 25 possibilities (10C2 + 5C2). The sample space for this random phenomenon would be:
{(Blue, Blue), (Blue, Red), (Red, Blue), (Red, Red)}

## A bag contains ﬁfteen balls distinguishable only by their colours; ten are blue and ﬁve are red. I reach into the bag with both hands and pull out two balls (one with each hand) and record their colours. What is the random phenomenon?, and What is the sample space?

Each combination has an equal chance or probability to occur when randomly selecting 2 balls from the bag. Additionally we could consider other attributes such as size and shape to further expand our sample space by including combinations such as “large blue and small blue” or “round red and oval red” but since we do not know these characteristics about our particular set of 15 distinguishable only by their colours we will stick just with colour for now. Thus our final sample space for this random phenomenon becomes:
{(Blue, Blue), (Blue, Red), (Red, Blue), (R

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