Probability (Set Theory)

1. Jan 21, 2009

vvvidenov

Suppose that one card is to be selected from a deck of 20 cards taht cointains 10 red cards numbered from 1 to 10 and 10 blue cards numbered from 1 to 10. Let A be the event that a card with an even number is selected; let B be the event that the blue card is selected; and let C be the event that a card with a number less than 5 is selected. Describe the sample spase S and describe each of the following events both in words and as subsets of S:
a) ABC
b) BCc
c) A U B U C
d) A(B U C)
e) AcBcCc
Please someone help me aboth the part how to describe the events in words

I did (a) ABC={even numbered blue cards less than 5}

total autcomes=20
S={ R1, R2, R3...R20}
A(even cards)={2,4,6,8,10}
B(blue cards)={B1,B2,B3...B10}
C(cards less than 5)={C1,C2,C3,C4}

ABC={even numbered blue cards less than 5}={ABC2,ABC4}
is that look okay.

b)B$$\bigcap$$Cc={5,6,7,8...10}
c)A U B U C= {1, 2...10}
d)A(B U C)={2,4,6,8,10}
e) AcBcCc={11, 12...20}
I am confused how to describe b) thru e). I know how to solve the problems, but describe in words I am not sure what to do. Please help. Thank you.

Last edited: Jan 21, 2009
2. Jan 21, 2009

NoMoreExams

For example doesn't that contain a red card that has a 5 on it?

3. Jan 21, 2009

vvvidenov

I think is okay, b/c B={1,2,3...10}
C={1,2,3,4}

The BCcc={5,6...10}.
It is the intersection B$$\cap$$Cc.
and the Cc is all numbers except C.

4. Jan 21, 2009

NoMoreExams

You need a better way to define things, you are using numbers to define B and C but B refers to colors whereas C refers to numbers

5. Jan 21, 2009

vvvidenov

Is it: BCc(blue cards numbered bigger than 5)={B6, B7...B10}

the notation confuses me a lot: is it {BC6, BC7...BC10} or only {B6, B7....B10}

Last edited: Jan 21, 2009
6. Jan 21, 2009

NoMoreExams

I would define my events as

A = {B2, B4, ..., B10, R2, R4,...,R10} i.e. cards that have even numbers on them - both blue and red

B = {B1, B2, ..., B10} i.e. all blue cards

C = {B1, ..., B4, R1, ..., R4} i.e. cards that have less than 5 on them - both blue and red.

So for part b) we want $$B \cap C^{c}$$ i.e. all the blue cards that are greater than or equal to 5 i.e. {B5, ..., B10}

Formally we could say

$$C^{c} = B_5, ..., B_{10}, R_5, ..., R_{10}$$

Now intersect that with B and you are left with $$B_5, ..., B_{10}$$

7. Jan 21, 2009

vvvidenov

Thank you so much for your help. I get it now. I did not realize that I was doing wrong the entire problem, not just the words description.