1. ## Union and intersection

43% of adults are stockholders. 75% of adult stockholders have some college education. 37% of adults have some college education. An adult is randomly selected.

What is the probability that the adult owns stock or has some college education?
S = stockholder, C = some college
P(S union C) = 0.43 + 0.37 - P(S int C) = 0.64, where P(S int C) = 0.43 * 0.37 = 0.1591. Is that right? Book's answer is 0.4775

What is the probability that the adult has neither some college education nor owns stock?
P(not S intersection not C) = (1-0.43) * (1-0.37) = 0.36
Thanks!

2. ## Re: Union and intersection

The book is right. Draw a Venn diagram and put 100 people total in the Adult circle.

3. ## The Following User Says Thank You to katxt For This Useful Post:

Regulus (03-17-2017)

4. ## Re: Union and intersection

Thank you! For the first problem I was using .37 in the intersection calculation, but should have used .75 of stockholders have some college. .43 + .37 - (.43 * .75) = 0.4775. So I should have used the completely contained subset to get the intersection result, and the venn diagram helped me see that.

But I haven't figured out how to set up the second problem. It looks like it should be just a simple intersection. Maybe I just need more practice and stats will eventually sink in, and it will be more like second nature. I arrived at the answer to the first problem empirically. Any further advice would be appreciated.

5. ## Re: Union and intersection

This type of problems are a classic to help students understand a little bit the role that conditional probability has in figuring out the probabilities of events. I have found that the classic 2 X 2 table set-up may be useful:

So far, you know this:

Code:
``````          | YES Education | NO Education |
------------------------------------------------
YES Stock |               |              | .43
------------------------------------------------
NO Stock  |               |              |
------------------------------------------------
|     .37       |              |  1``````
And you also know 75% of adult stockholders have some college education. So that if a randomly-selected adult owns stock, you also know the probability that they have a college education. In other words, you know that the probability that an adult has some college education GIVEN that (s)he owns stock, is 0.75.

Can you fill-out the table now? Notice that answering question #2 is equivalent to finding what goes in the lower-right square of the 2X2 table, the NO Education and NO Stock cell.

I feel that you're getting lost in the fact that college education and owning stock are not independent events.

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Regulus (03-18-2017)

7. ## Re: Union and intersection

Awesome! I figured I should make a table and was thinking a row would have to be stockholders and a column would have to be education. But it wasn't making sense because I wasn't splitting the two into 'yes' and 'no'. 0.43 * 0.75 = 0.3225 in the Yes Stock, Yes Ed cell. In the No Stock row 0.0475 + 0.5225 = 0.5700, which when added to 0.43 = 1. Thanks!

Teaching myself with little spare time. Hopefully this time next year I'll be a wiz and can help out here.

8. ## Re: Union and intersection

Originally Posted by Regulus
Awesome!...Hopefully this time next year I'll be a wiz and can help out here.
Nice to see that you are understanding the concepts.

That said, do not start a sentence with word "Hopefully."

Hopefully you will stop doing this.

You should scribe; "With hope, this time next year....".

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