Independent & Dependent Compound Events

Independent & Dependent Compound Events

Number Cubes and Marbles

Opening

Number Cubes and Marbles

Look at these three problems and consider the following:

  • You roll 2 number cubes. What is the probability that you will roll double 6s?

  • You draw 2 marbles from this bag. What is the probability that you will draw two red marbles?

  • What is different about these two multistage experiments and compound events?

Independent Events

Opening

Independent Events

Discuss the following with your classmates.

  • Two events are said to be independent if the outcome of one event does not influence the outcome of the other event.
  • Two events are said to be dependent if the outcome of the one event does influence the outcome of the second event.
  • An example of a dependent event is if you draw an ace from a deck of cards and do not replace it. After drawing the ace, the deck has one less ace than it did before. Thus, the probability of drawing an ace on the second try has been affected by the outcome of first event.

Math Mission

Opening

Draw a diagram to determine the probability of dependent compound events.

Independent or Dependent Events

Work Time

Independent or Dependent Events

Which of the following events are independent and which are dependent? Explain your answer.

  • There are 4 oranges and 12 apples in a bowl. You reach in and randomly take a piece of fruit to eat. Then you randomly get another piece of fruit.
  • You toss a coin and roll a number cube.
  • You reach into your drawer and pull out one sock. You reach in again and pull out the same color sock.
  • You spin spinner A twice. You want to spin an even number and then an odd number.
  • You spin spinner B twice. You want to get the same color both times.

Counters

Work Time

Counters

You have a box containing four counters numbered 5, 6, 7, and 8. You randomly choose one counter.

  • How many outcomes are there in the sample space?
  • What is the probability that you will select the 5?
  • If you select the 5 and do not replace it, how many outcomes will there be in the new sample space?
  • Based on this new sample space, what is the probability of selecting a 6?
  • Illustrate your thinking with a tree diagram, a list, and/or a table.
  • What is the probability of first selecting the 5 and then selecting the 6, assuming that you do not replace the first counter?

Marbles

Work Time

Marbles

You have a bag of 3 red marbles and 2 blue marbles. You draw 1 marble without replacing it and then draw a second marble.

  • Show the sample space using a tree diagram, a list, and/or a table.
  • What is the probability that you will draw a red marble and then a blue marble?

Challenge Problem

You have 10 cards numbered 0–9, lying face down. If you draw 2 cards to form a two-digit number, and you do not replace the first card, what is the probability that you will form the number 63?

  • Explain your method for solving this problem.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ diagrams and solutions.

As your classmates present, ask questions such as:

  • How did you decide which events are independent events and which are dependent events?
  • How does your representation of the sample space for dependent events differ from your representation of independent events?
  • How would the probability differ if the two selections were independent versus dependent?

Independent and Dependent Compound Events

Formative Assessment

Summary of the Math: Independent and Dependent Compound Events

Write a summary about independent and dependent compound events.

Check your summary:

  • Do you define independent events and give an example?
  • Do you define dependent events and give an example?
  • Do you explain how finding the probability of independent events differs from finding the probability of dependent events?

Reflect on Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

I would describe the difference between independent events and dependent events as…