Compound Events Examples

Using an organized list, figure out the probability of drawing the queen of hearts from a stack of red (hearts and diamonds suits only) face cards and then drawing a red marble out of a bag with 2 red marbles and 3 black marbles.

The first 2 letters will represent the card drawn, with H representing hearts and D representing diamonds, K representing king, Q representing queen, and J representing jack. The letter/number pair will represent the marble.

Now we can count the number of desired outcomes and count up the total outcomes. There are two ways to draw a queen of hearts and a red marble, and there are 30 outcomes in all so the probability is or 6.6%.

The latest and greatest activity at your family pizza party is to grab a piece of pizza without looking, from a box of pizza with all of the flavors mixed up, and then doing the same with a box of donuts. Your family always orders cheese pizza, pepperoni pizza, meat lover’s pizza, and veggie pizza, and they get chocolate donuts, powder donuts, and jelly donuts. Using a tree diagram, determine all the possible outcomes for this food-grabbing experience.

This tree diagram is going to start with the pizza choices first and the donut choices second, but you can do it either way.

For each of the 4 pizza choices there are 3 donut choices, making 12 total outcomes possible.

Use the area model to determine the probability of rolling a multiple of 3 on a die and then flipping heads on a coin.

There are only 2 numbers on a die that are multiples of 3, the number 3 itself and the number 6, but there are 6 total numbers on a die so the grid will have 6 columns. Since there are only two outcomes for flipping a coin, the grid will have 2 rows.

There are 12 total outcomes, and only 2 of them involve flipping a head and rolling a multiple of 3. So the probability is or 16.6%.