Source: Marbles, Joe Mabel, Wikimedia
Now let's look at how an area model can help to solve compound probability situations. We'll return to our red and green marble problem from earlier.
Source: Marbles, Joe Mabel, Wikimedia
A jar has 6 red marbles and 4 green marbles. Two marbles are drawn without replacement from the jar. What is the probability that both of the marbles are green?
We can use the coordinate grid and area to solve this problem. This works well for AND situations.
First, we create a grid that represents the sample space. In this case, we know the first draw will be from 10 marbles and the second draw from 9 marbles, so the total samples space is 10 x 9.
Next, plot the area of the second draw: 3 green marbles out of a possibility of 9.
The area where the two draws over lap is the probability of the combined events.
Sandra has a bag of 12 marbles that are identical in size. The bag contains 7 yellow marbles and 5 pink marbles. Determine the probability that she will first draw a pink marble then a yellow marble. Use the Probability applet below to plot the information from your problem.
Interactive popup. Assistance may be required.
Roberto created a game board for his little brothers and sisters to play. To determine if they advance on the game board he put 12 blue and 8 green blocks in a bag. Each player gets to draw two blocks. Determine the probability of first drawing a blue block, replacing it, then drawing a green block. Use the Probability applet below to plot the information from your problem.
Interactive popup. Assistance may be required.
