Thirty students in the fifth grade class listed their hair and eye colors in the table below: brown hair blonde hair total green eyes 9 6 15 brown eyes 10 5 15 19 11 30 are the events "brown hair" and "brown eyes" independent?

No, the events "brown hair" and "brown eyes" are not  independent.

Step-by-step explanation:

The table that represents the  hair and eye colors of thirty students of the fifth grade are given in table as:

                         Brown hair          Blonde hair              Total

Green eyes           9                       6                               15

Brown eyes          10                       5                              15

Total                     19                        11                             30

No, the events  "brown hair" and "brown eyes" are not independent.

Since, two events A and B are said to be independent if:

P(A∩B)=P(A)×P(B)

where P denotes the probability of an event.

Here we have:

A= students having brown hair.

B= students having brown eyes.

A∩B= students having both brown hair and brown eyes.

Now,

P(A)=19/30  (ratio of addition of first column to the total entries)

P(B)=15/30  ( ratio of addition of second row to the total entries)

Also,

P(A∩B)=10/30

Now as:

P(A∩B) ≠ P(A)×P(B)

Hence, the two events are not independent.

it's both, now can you answer my most recent question?

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages