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lora16 [44]
3 years ago
13

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?
Mathematics
1 answer:
Mars2501 [29]3 years ago
8 0

Answer:

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.

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Answer:

A) t = -3

Step-by-step explanation:

We have the expression \frac{(t-12)}{2}=\frac{3t}{2}-3 and we have to find the value of t.

First we are going to reorder the expression:

\frac{(t-12)}{2}=\frac{3t}{2}-3\\\\3=\frac{3t}{2}-\frac{(t-12)}{2}\\\\3=\frac{3t-t-(-12)}{2}\\\\3=\frac{2t+12}{2}

Now we have to multiply each side by 2,

3=\frac{2t+12}{2}\\\\3.2=\frac{2t+12}{2}.2\\\\6=2t+12

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Divide both sides in 2,

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The answer is option A) t = -3.

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