Question

Fifty students in the third grade class listed their hair and eye colors in the table below:

Answer 1

Brown hair Blonde hair Total
Blue eyes 14 8 22
Brown eyes 16 12 28
39 20 50

Are the events "blonde hair" and "blue eyes" independent?
Yes, P(blonde hair) • P(blue eyes) = P(blonde hair ∩ blue eyes)

Yes, P(blonde hair) • P(blue eyes) ≠ P(blonde hair ∩ blue eyes)

No, P(blonde hair) • P(blue eyes) = P(blonde hair ∩ blue eyes)

No, P(blonde hair) • P(blue eyes) ≠ P(blonde hair ∩ blue eyes)

Answer 2

@mathmale !

Answer 3

We need to check if that equation holds or not - so we need to find a few things like P(blonde hair) How many people are there in total?

Answer 4

50?

Answer 5

Right! And how many of those have blonde hair?

Answer 6

20

Answer 7

right! So...
P(blonde hair) = 20/50
P(blue eyes) = 22/50
Agree?
Now we are trying to find P(blonde hair AND blue eyes) right now
that is where we are at.

Answer 8

p(Blonde hair and Blue eyes) = ?

Answer 9

Would that be 8?

Answer 10

Yup, so it would be 8/50. :)

Answer 11

so now you have all these probabilities
so now you can check if the equation holds

Answer 12

plug your numbers into that equation and see if that equation holds please

Answer 13

OK, but how do I plug the numbers in? And to what equation?

Answer 14

p(blonde hair)*p(blue eyes) = p(blonde hair and blue eyes)
that is the equation you need to determine if it is true
you know each of those probabilities just plug the values into the right spots and see if the equation holds.

Answer 15

These are the probabilities:

P(blonde hair) = 20/50
P(blue eyes) = 22/50
P(blonde hair and blue eyes= 8/50

Answer 16

Oh, if its independent or not? So since 20 and 22 don't add up to 8, then it is independent?

Answer 17

the equation require you to multiply everything out
20/50 * 22/50
does that equal 8/50 ?
that is what you need to determine right now

Answer 18

so what does 20/50 * 22/50 equal?

Answer 19

No, it doesn't. 440/50

Answer 20

the bottom should be 50*50 right?
or 2500

Answer 21

so does 440/2500 equal 8/50 ?

Answer 22

right, sorry!
No, so what does that mean?

Answer 23

so hopefully you stick with your answer from before and tell me that
p(blonde hair)*p(blue eyes)
is not the same thing as
p(blonde hair and blue eyes)
the fractions end up giving you something different on both sides
so the equation didn't hold so looking at your answer choices, it is either B and D

Answer 24

so does this mean these events are independent ?
when that equal fails to hold, does that mean they are independent?

Answer 25

so the answer is no here, they are not independent -- D
they aren't independent because that equation isn't correct. :)

Answer 26

I would say no.

Answer 27

great! :)

Answer 28

Oh great, thanks for your help:)

Answer 29

its fine