compound probability 2?

Before getting started, let's define probability is

What You Want

------------------------

What You Get

This definition is not precise enough for math and stat purposes. So we pick another definition. We also say that N(something) means number of somethings.

Or new definition of probability suited for math use is now

N(ways of getting what you want)

-------------------------------------------------

N(ways of getting what you get)

Let's start on the first prob

1) What is the probability of picking a balloon with yellow or white on it?

We know that N(balloons) = 1000 because its given. We also know the balloons are multicolored because that is given.

The trouble is the statement picking a yellow balloon OR a white balloon.

The reason we have trouble is because OR in the math/stat sense is different than the or used in everyday life. For example, if you told someone you were going to wear a grey skirt or red shoes, you would wear either a grey skirt or a red shoes but not both.

However, if you use a math/stat OR, you'd could wear the grey skirt, the red shoes or both. You'd wear one or the other or both. Since we a doing a math/stat problem, we have to use the math/stat OR, which I'll use the symbol OR. Sometimes this OR is called a logical OR

There is a rule for the probability of A or B. It is:

P(A OR B) = P(A) + P(B) - P(A & B)

The & means AND or logical AND. A logical AND is pretty much like the and in everyday life. If you said you were going to wear a green dress and black shoes, you'd put on the green dress and the black shoes.

Note the - P(A&B) term. This term is included because OR double counts when A&B happen

Now let's apply all this to finding

1) P(yellow balloon OR white balloon) = P(YB OR WB)

We now write

P(YB OR WB) = P(YB) + P(WB) - P(YB&WB)

Start with P(YB)

P(YB) = N(yellow balloons) / N(Balloons)

Find N(yellow balloons). This means we count all balloons that have some yellow *regardless of what other color they may have*. We are given:

150 red and *yellow* balloons

300 *yellow* and white,

200 *yellow* and blue

for a total of 650 yellow balloons

N(Balloons) = 1000 (Given)

Therefore P(YB) = 650 / 1000 = 0.65

Now compute P(WB)-

P(WB) = N(white balloons) / N(Balloons)

Find N(white balloons). This means we count all balloons that have some white *regardless of what other color they may have*. We are given:

300 yellow and *white*,

100 *white* and red

for a total of 400 white balloons

N(Balloons) = 1000 (Given)

Therefore P(WB) = 400 / 1000 = 0.40

What remains is P(YB & WB). Set this up

P(YB & WB) = N(Yellow AND White Balloons ) / N(Balloons)

From the data,

300 yellow and white *yes*!

P(YB & WB) = 300 / 1000 = 0.30

Now recall:

P(YB OR WB) = P(YB) + P(WB) - P(YB&WB)

P(YB) = 0.65

P(WB) = 0.40

P(YB OR WB) = 0.30

Answer is

P(YB OR WB) = 0.65 + 0.40 - 0.30

P(YB OR WB) = 0.75

2) What is the probability of picking a balloon without blue or red on it?

This is P(NOT-blue (NB) OR NOT-red (NR)) or

P(NB OR NR) = P(NB) + P(NR) - P(NB & NR)

Find P(NB)

P(NB) = N(NB) / N(balloons). Pick balloons that not blue *regardless of what the other colors are*

150 red and yellow balloons - *Not Blue*!

100 white and red balloons - *Not Blue*!

300 yellow and white - *Not Blue*!

Total for NOT blue is 550

P(NB) = 550/1000

P(NB) = 0.55

Now find P(NR)

P(NR) = N(NR) / N(balloons). Pick balloons that not red* regardless of what the other colors are*

300 yellow and white - *NOT Red*!

200 yellow and blue - *NOT Red*!

Total is 500

P(NR) = N(NR) / N(balloons)

P(NR) = 500 / 1000

P(NR) = 0.5

Now find P(NB & NR)

P(NB & NR) = N(NB & NR balloons) / N(balloons)

We are only interested in balloons that are both NOT-red AND NOT-blue, *regardless of anything else*

300 yellow and white - *both NOT-red AND NOT-blue*!

P(NB & NR) = 300 / 1000

P(NB & NR) = 0.3

Recall that

P(NB OR NR) = P(NB) + P(NR) - P(NB & NR)

P(NB) = 0.55

P(NR) = 0.5

P(NB & NR) = 0.3

P(NB OR NR) = 0.55 + 0.5 - 0.3

P(NB OR NR) = 0.75

Note: The text says "Multicolored balloons come in a package of 1000". This means that the balloons have more than one color on them. Since only two colors per balloon are specified, we assume that each balloon has two colors.

It means that 150 of the ballons are some red and some yellow.

1. Yellow and white is 300 so 300/1000 = 3/10

2. blue + red = 250

not blue and red is 1000-250=750

750/1000=3/4

1)

yellow or white is (150+300+200) + 100 = 750 in 1000 or 75% or .75

the first terms are the number with yellow, the last the number with white, BUT you can't count the 300 yellow and white twice!

2)

No blue or red is 300 in 1000 = 30% = .3

This is the only what to get no blue or red (by getting one of the 300 that is yellow and white.)

Hope this helps!

a million. There are 75 balls, consequently there are (75 - a million)/2 even balls or 37 even balls P = 37/75 X 36/seventy 4 X 35/seventy 3 X 34/seventy two X 33/seventy one = .0.5 2. There are 29 numbers under 30, 15 of that are atypical, and 14 of that are even. So complete style of applicants = 37 - 14 + 29 = fifty two P = fifty two/75 X fifty one/seventy 4 X 50/seventy 3 X 40 9/seventy two X 40 8/seventy one = 0.15

3/4

3/10