# Probability for compound events

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##### Intros

###### Lessons

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##### Examples

###### Lessons

**Compound event outcomes and probability trees**

Fill in the probability tree and list the outcomes for:**Probability of compound events**

Find the probability for:- Using a three-part spinner and:

- spinning yellow twice in a row.
- spinning blue once and red once.
- spinning yellow first and then red second.

- Flipping a coin then spinning a two-part spinner and:

- The coin lands on head, and the spinner lands on red.
- The coin lands on tail, and the spinner lands on blue.

- Spinning the arrow on spinner #1 then on spinner #2 and:

- both spinner #1 and #2 land on red.
- one spinner lands on red and the other lands on blue.
- spinner #1 lands on yellow, spinner #2 lands on blue.

- Using a three-part spinner and:
**Probability for compound events: word problem**

In a board game, each player needs to roll two dice at the same time during their turn.- How many total outcomes are there?
- There are bonus points for rolling some combinations in this game. What are the probabilities of:
- Rolling two-6s.
- Rolling two of the same number.
- Rolling a sum greater than 8.
- Rolling a sum less than 4.

- Which outcome for bonus points is the most likely for this game? Use the answers from the previous part.
- Using theoretical probability, write the expected results.
- If you roll the dice 36 times, how many times will you roll one 5 and one 6?
- If you roll the dice 360 times, how many times will you roll two-6s?
- If you roll the dice 120 times, how many times will roll two of the same number?

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###### Topic Notes

In this lesson, we will learn:

- Compound probability is for finding the chances of an event involving two simple probability scenarios
- How to draw a probability tree to show all possible outcomes for a compound event
- How to use an outcome table to show all possible outcomes for a compound event
- How to calculate compound probability fractions

__Notes:__**Compound probability**(or**probability for compound events**) is the chances of an event—involving two probability scenarios—happening.- Some examples of compound situations: flipping 2 coins, rolling 2 dice, spinning the arrow on 2 spinners, or (combinations like) a coin flip and a die roll.
- Showing all possible outcomes for compound events will be different than
**probability for simple events**. A**probability tree**or**outcome table**can be used - A
**probability tree**can be drawn vertically or horizontally. Each level represents each simple event: start at a point and draw branches for all possible outcomes. At the next level, the end of each previous branch will be a new starting point. Draw branches for all possible outcomes for the second simple event.

- Another way to find all outcomes for compound events is by using an
**outcome table**, crossing all outcomes for the first event in the rows, by all the outcomes for the second outcomes in the columns.

- The total number of outcomes can be calculated:

*total outcomes*= (*#outcomes*1^{st}*event*) × (*#outcomes*2^{nd}*event*) - The formula $P$ (
*event*) = $\frac{number\,outcomes\,wanted} {total\,number\,possibilities}$ can also be used for compound probability - Or, using fraction multiplication, compound probability for an event can also be found using the formula:

*Compound Probability*= $P$ (1^{st}*event*) × $P$ (2^{nd}*event*)

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