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### Course: 7th grade (Illustrative Mathematics)>Unit 8

Lesson 5: Lesson 8: Keeping track of all possible outcomes

# Sample spaces for compound events

Explore the notion of a "sample space". See a sample space represented as a tree diagram, table, and list.

## Want to join the conversation?

• Can you present the information of a sample space diagram differently?
.Are the different methods of showing this information
(except from the ones shown of course)
• Another method you can use to find the number of possible outcomes is to multiply the outcomes. For example, since there are 3 flavors and 3 different sizes you can multiply 3 x 3 which is 9, and also means that there are 9 possible outcomes.
• at what is that box thing Sal drew
• He put a box around the math to make it show out more than the other things he wrote.
• has anyone ever thought of stopping this video and then going out to get cupcakes then come back and continue watching the video eating cupcakes?;)
• Write that down, WRITE THAT DOWN!
• "I encourage you to pause the video and work this out on your own"
• i don't have to the questions in the video are relatively easy LOL
• The probability of the first coming up a 3 is the sum was less than 7?
• Can't U just do 3 *3 because 3 *3 =9 . Since there is 3 options each ones of the 3 flavors
• At , shouldn't Sal have said, "Chocolate, Vanilla, and Strawberry?"
• I don't get the difference between the three. For example a + b + c = d. D is still the sum when a + c + b. Multiplication is the same. 8 * 9 * 34 = 34 * 8 * 9. Hope this makes sense.
• How many numbers are in 6 dices combined together?
• If it is a four-sided dice, then there are 24 numbers. If it a six-sided dice, then there are 36 numbers.
• then what is the difference between {ht,th} and {ht} in sample space for coin having? i am confused ht and th are same or different
if yes then why in above video there is not sample space for choclate small but only small choclate
• Yes there is a difference between HT and TH in that a coin (or two coins) are being flipped
the difference can show up most easily in the question asked, for example,
What is the probability of flipping a fair coin twice and getting a heads then a tails? (1/4 because order does matter)
What the is probability of flipping a coin twice and getting one heads and one tails? (1/2 because order does not matter)
As to your second question which seems intuitive, the problem is that the sample space is created by flipping a coin twice, it just so happens that there are only two choices on a coin, so four possibilities (h first, h second)(h first, t second)(t first, h second) and (t first, t second) - the ht and th are not just interchanged, they are 2 different possibilities
The problem of small and chocolate is that the sample space is built on flavors and size, so chocolate small and small chocolate are really the same possibility rather than two distinct possibilities (he did two tree diagrams which show the 9 outcomes which just shows these are the same)
Hope this helps