Question

Stats Question please help!

Answer 1

I think they are independent, but does it matter that the males have more who make over 50,000 ?

Answer 2

when it says "the person" in --> P(being female | the person earns over $50,000) = P(being female)
does that mean females and males too?

Answer 3

Melissa, you 'll need to post (share) the entire table first. This is a problem in "conditional probability." by the way.

Answer 4

in the attachment?

Answer 5

Yes. You did share an illustration, but the bottom part of your table was cut off.

Answer 6

i could see entire table....


First find the probability of P(being female) = # female / total people.

Answer 7

Then Find the probability that
P (person earns over 5k) = # people earning over 5k/ total # of people

Answer 8

i am trying to use this formula
\(\Large P(A \cap B) = P(B) P (A|B)\)

Answer 9

ok, so
(.45) = 450/1000

then
by person earns over 5k you mean female, uhm right?

Answer 10

no, among all person, male or female, earning over 5k

Answer 11

Note: The formula provided by hartnn is entirely appropriate for solving this problem. However, the contingency table provided constitutes another approach to solving this problem, one that for some people (including myself) is a bit less abstract.

Answer 12

ok, so then you would have
P (person earns over 5k) = # people earning over 5k/ total # of people
(0.85) = 850/1000

Answer 13

yeah, thats correct.

so now we have enough data to find
P(being female | person earns over 5k)
can you use my formula and find it ?

Answer 14

ok, so what are a and b?

Answer 15

A = being female
B = person earning over 5k

Answer 16

ok

Answer 17

you'd need
P(being female \(\cap \) person earns over 5k)

Answer 18

which is P (female earning over 5k)

Answer 19

so
P(A∩B) = P(0.85*0.45)
so 0.3825 ?

Answer 20

are they independent events, though?

Answer 21

why did you use
\(P(A \cap B) = P(A) \times P(B)\)
thats true only when A and B are independent, and thats what we are trying to figure out!

Answer 22

P (female earning over 5k)
find this from the table

Answer 23

P (female earning over 5k) = # females earning over 5k / total # people

Answer 24

### maybe a shorter way is to find P(A), P(B), P(A \(\cap \)B) and check whether \(P(A \cap B) = P(A) \times P(B)\) holds true :P ###

Answer 25

okay.... so
(A∩B) = P(0.85*0.45) = 3825
P(A) is 0.45
P(B) is 0.85
?

Answer 26

we need to find (A∩B) from the table!

P(being female ∩ person earns over 5k)
= P (female earning over 5k) = # females earning over 5k / total # people

Answer 27

OH
okay, so 450 / 1000

Answer 28

so 0.45 ?

Answer 29

no...450 is total females
we need # females earning over 5k!

Answer 30

okay, i am feeling really stupid now, sorry :\
375/1000
3.75

Answer 31

0.375
and it happens, no problem :)

Answer 32

(remember probability cannot exceed 1)

Answer 33

ah, so i messed up again :|
lol today is not my day
that is so true

Answer 34

use this now
\(\Large P(A \cap B) = P(B) P (A|B)\)

and find
P (being female | person earning over 5k)

Answer 35

so, now I multiply? or not?

Answer 36

P (being female ∩ person earns over 5k) = P (person earns over 5k) * P (being female | person earning over 5k)

Answer 37

we already have found
P (being female ∩ person earns over 5k)
and
P (person earns over 5k)

Answer 38

0.375 = 0.85 *P (being female | person earning over 5k)

Answer 39

P (being female | person earning over 5k) = 0.375/0.85

Answer 40

is that equal to P (being female) ??

Answer 41

I got 0.44117 so no?

Answer 42

correct!
since they are not equal, the events are dependent!

Answer 43

yay! okay, thank you! :D

Answer 44

lets ask @mathmale if he has a shorter/more intuitive approach for this...

Answer 45

ok :)

Answer 46

Criterion for independence of these two events: The probability that the person chosen at random from the sample of 1000 is female, GIVEN THAT THAT PERSON EARNS MORE THAN $50K per year, is equal to the probability that the person chosen at random is female.

If this is not the case, then the two events ARE dependent.

Looking at the table, we see that a total of 850 people in 1000 earn over $50K per year. Of these, how many are female? 375.

Therefore, P(female | over $50K) = 375/850 = 0.441.

And: P(female) = 450 / 1000 = 0.45

Since these two probabilities are different, BEING FEMALE and EARNS OVER $50K/YEAR are DEPENDENT (which obviously also means NOT INDEPENDENT).