Question 1207193: A special deck of 16 cards has 4 that are blue, 4 yellow, 4 green, and 4 red. The four
cards of each color are numbered 1 through 4. A single card is drawn at random. Define
events
B: the card is blue
R: the card is red
N: the number on the card is at most two
(a) List the outcomes that comprise B, R, and N. (Use notation like B3 to represent a
blue card with a 3 on it.)
(b) List the outcomes that comprise B ∩ R, B ∪ R, B ∩ N, R ∪ N, B, and B ∪ R.
(c) Assuming all outcomes are equally likely, find the probabilities of the events in the
previous part.
(d) Determine whether or not B and N are mutually exclusive. Explain why or why not.
3. (O7) In early 2001, the United States Census Bureau started releasing the results of th
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
The deck = {B1,B2,B3,B4,Y1,Y2,Y3,Y4,G1,G2,G3,G4,R1,R2,R3,R4}
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(a)
I'll do B and R in the (a) part for you:
B = {B1,B2,B3,B4}
R = {R1,R2,R3,R4}
You do the N part. Here's how:
N = ?. If the number on the card is at most two, then that number is either 2,3,
or 4. So look through the deck and list all the cards that have a 2,3, or 4 on
them regardless of what letter it has before the number. List them all between
braces {} with commas separating them.
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(b)
B ∩ R = ?. Are there any blue cards that are also red cards? If so list
them between braces {} with commas separating them. If not, write the empty set
∅ or { },
B ∪ R = ?. List all the cards that are either in B and/or in R between braces
{}, with commas separating them.
B ∩ N = ?. Are there any cards that are both in B and N? If so, list them
between braces {} with commas separating them. If not, write the empty set
∅ or { },
R ∪ N = ?. List all the cards that are either in R and/or in N between braces
{}, with commas separating them.
B = ?. Just copy what I gave you above for B.
B ∪ R = ?. List all the cards that are either in B and/or in R between braces
{}, with commas separating them.
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(c) In each of these, count the number of cards in the set which the probability
is asked for. Write this as the numerator of a fraction. Then count the number
of cards in the deck, and write this as the denominator of the fraction. Reduce
the fraction if possible. This will be the answer in each case.
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(d) Sets are said to be "mutually exclusive" when they have NO elements in
common. [The word "exclusive" is not to be taken as what "exclusive" usually
means. When you see the words "mutually exclusive", think of the word
"exclusive" and though it were the word "excluding" instead. It means that each
of the two sets 'excludes' all (does not contain any) of the members or elements
of the other set.]
So use that to answer (d).
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(3) Looks like you copied and pasted too much. LOL
Edwin
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