6th Grade Math Textbook, Progress

Find the probability: (a) if the first choice is replaced;

and (b) if the first choice is not replaced.

Experiment: Pick one marble from a box containing 3 yellow (Y) marbles, 2 white (W)

marbles, and 1 red (R) marble. Then pick a second marble.

5. P(R, Y) 6. P(Y, R) 7. P(Y, W) 8. P(R, Y or W)

Draw a tree diagram or make a table and use the Counting Principle

to find the number of possible outcomes. List all possible outcomes.

1. Toss a penny and roll a 1–6 2. Spin the spinner and choose
   number cube. a marble without looking.


2. Make a sandwich with 5 different 4. Put together an outfit from a selection of
   types of bread and 2 different fillings. 4 shirts, 2 pairs of pants, and 2 sweaters.

1

2

6

AB

DC

Independent and Dependent Events

A bag contains 10 cubes: 5 red, 3 blue, and 2 green.

Pick 2 cubes from the bag without looking. What is the

probability of picking a blue cube and then a red cube?

To find P(blue, red), multiply: P(blue)
P(red)

Pick the first cube. Return it to the bag. Then pick the second cube.

These events are independent events.

The first event does not affect the second event.

If Aand Bare independent events, P(A, B)P(A)
P(B).

P(blue, red)P(blue)
P(red) 130 
 150  230 

Pick the first cube. Do not return it to the bag. Then pick the second cube.

These events are dependent events.

The first event does affect the second event.

If Aand Bare dependent events, P(A, B)P(A)
P(B after A).

P(blue, red)P(blue)
P(red) 130 
^59 ^16 

2

1

2 3

1 1

1 less cube in bag

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