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## Statistics and probability

### Course: Statistics and probability>Unit 7

Lesson 2: Probability using sample spaces

# Subsets of sample spaces

Sal solves an example about subsets.

## Want to join the conversation?

• At , these questions should be reworded as "the subset consists of ONLY outcomes where...". to represent Sal's logic, otherwise this is not grammatically correct. The sample subset DOES contain ALL the outcomes where your friend wins OR there is a tie. It's extremely confusing and it is used in the quiz after the video as well. • My thoughts are the same as yours. I believe that what Sal explains is not correct. The first 3 statements are actually to tell us to check what's not included in the subset to see whether or not they contain what meets the question. And if it does, then the statement is false - because the subset doesn't contain all stated outcomes. Based on this logic, the correct answer is No. 4 still.
• Question: is there a practice task called "Describing subsets of sample spaces"? I was told to do this by my teacher but I can't find it; I can only find this video. Also, it was recommended for me but does not load. I try to do it and it sends me back to the homepage. Thanks! • Around , he talks about option one, "The subset consists of all the outcomes where your friend does not win."

To me, that does not require all the outcomes selected to be ones in which your friend does not win, but rather that the subset contains all the possibilities in which your friend does not win. It could include all the possibilities in which your friend does not win, plus some. His reasoning for not selecting that option was that the subset includes an outcome in which your friend does win. This seems faulty to me.

That is how I read that option on a purely grammatical level. Is there some mathy jargon I am missing here? • also, does it matter in what order you write the different outcomes? • is there also an equation for these kind of problems without making a chart? • Well, you CAN write it formally without using a chart, but you would still need to solve the probabilities in your head.

For the Harry Potter example, you would write the first option as P (Holly ∪ Unicorn) - That U in the middle means you're calculating a total probability (it really means "union", as you've probably seen when dealing with inequalities in algebra). That can be solved as P(Holly) + P(Unicorn) - P(Holly and Unicorn happening together). This is where you need to make your chart in your mind: How many times can a Holly wand happen? How many times can a Unicorn wand occur? And lastly, how many times can a Holly wand and a Unicorn wand happen together at the same time? You know a Holly wand can happen 5 times out of 20, so P(Holly) = 5/20. A Unicorn wand can happen 4 times out of 20, so P(Unicorn)= 4/20. And a Holly AND Unicorn wand can only happen one time out of 20, so P(Holly AND Unicorn) = 1/20.

Getting back to our original equation, P(Holly) + P(Unicorn) - P(Holly and Unicorn happening together) = 5/20 + 4/20 - 1/20 = 8/20. And that's the same result you get when considering the chart.

P.S.: You're subtracting the P(Holly and Unicorn) because you're counting that outcome twice, when considering the single probabilities of P(H) and P(U).
• It says: "The wand that selects Harry will be made from of holly or unicorn hair."
Wouldn't this exclude the wand that is both? I mean, shouldn't "holly OR unicorn" mean that it can't be both? (It is either holly or unicorn) • I am still a little confused. What does subsetes even mean? • In this case, the word "set" means the set of all possible outcomes. in the case of flipping a coin, the set of possible outcomes is either heads or tails. A subset is a smaller set of outcomes that is contained in that larger set. So if you are rolling a die and what to know the probability of getting an odd number, you are looking at the subset that contains all the outcomes in which the die comes up with an odd number (1, 3, and 5). Hope that helps!
• A quick question:
Thank you!
Simon
(1 vote) • I really don't understand in the first example why the or is 8/20 and not 9/20. It said Holly OR Unicorn hair. The chances of picking Holly would be 5/20, and the chances for unicorn hair would be 4/20. If you add those you get 9/20 and not 8/20. So what's the deal? I know he refused to count the Holly and Unicorn twice but I don't get why. It is like you are only counting the Unicorn 3 times then...
(1 vote) • There are 5 wands that use Holly. That's 5/20 wands. Then there are 4 wand's that use Unicorn Hair. However, one of the wands that uses Unicorn Hair also uses Holly. Since there is only one wand with Holly and Unicorn Hair and its already been counted (when we counted the ones with Holly), we can't count it again. Therefore, we have 3/20 wands. Adding that to our 5/20 wands, we get 8/20 = 2/5. You probably already knew that. I just wanted to be sure we were on the same page.

Now, think about if there were only one wand, and it was made with Holly and Unicorn. That's 1/1 wands with Holly and 1/1 wands with Unicorn. 1/1 + 1/1 = 2 wands, but that doesn't mean that there are two wands. We simply have counted one of the wands twice. That is what Sal is doing when he skips that wand the second time around. Makes more sense? 