Training Camp

In this lesson, you will explore probability with both dependent and independent events. You must first be able to classify an event as dependent or independent. The easiest way to differentiate them is to look at examples in each category. Recall from Warm Up that dependent events affect each other and independent events do not.

Examples of independent events :

• Flip a coin and roll a six-sided die.
• Pull a marble from a bag of three marbles and pull a card from a deck of face cards.
• List the gender of the first and second child born in the same family.
• Pull a card from a standard deck, replace it and pull a second card.

Because the objects in these examples are all discrete, they do not affect each other. In the last example, replacing the card means the first draw does not affect the second.

Examples of dependent events :

• Choose a cube from a bag of ten cubes. Do not replace it, and then choose another cube.
• Choose two students from the same class.
• Choose six numbers for a lottery.
• Pull a card from a standard deck, but do not replace it before pulling a second card.

These examples have one fewer object to draw from on the second turn because the first object chosen is not replaced.

In the language of probability, an experiment is an action that has measurable results. All examples above are mathematical experiments. Recall from Unit 2 that the set of all possible outcomes of an experiment is the sample space for the experiment. Consider the example, Flip a coin and roll a six-sided die . What is the sample space for flipping the coin and rolling the die? To illustrate this sample space, use a tree diagram. The first task is to flip the coin. Because two outcomes are possible, the tree diagram has two branches. The outcomes are shown as H for heads and T for tails. The second task is rolling the die. Six outcomes are possible, so the tree diagram has six branches coming from both H and T. The outcomes are shown as 1, 2, 3, 4, 5, and 6.