Information for question 1-2. One-half of the students at Greendale Middle School take art. Two-thirds of students take Spanish. Jenny uses a coin and a standard number cube as a simulation of the students at Greendale Middle School. Jenny let's "T" represent a student taking art and "H" represents a student not taking art. She lets the numbers 1 2 3 and 4 on the number cube represent a student taking Spanish and the numbers 5 and 6 represent a student not taking Spanish. This is the table:
http://gyazo.com/cb9fd2a2f5ff44a80f719e025b7abd69

Question

Information for question 1-2. One-half of the students at Greendale Middle School take art. Two-thirds of students take Spanish. Jenny uses a coin and a standard number cube as a simulation of the students at Greendale Middle School. Jenny let's "T" represent a student taking art and "H" represents a student not taking art. She lets the numbers 1 2 3 and 4 on the number cube represent a student taking Spanish and the numbers 5 and 6 represent a student not taking Spanish. This is the table: 
http://gyazo.com/cb9fd2a2f5ff44a80f719e025b7abd69

anonymous · Answer

Find the probability that a student a Greendale middle school takes both art and spanish
3/20
2/5
7/20
1/10

loser66 · Answer

@e.mccormick

anonymous · Answer

Find the probability that a student a Greendale middle school takes neither art nor spanish
3/20
2/5
7/20
1/10

texaschic101 · Answer

according to the table...32 are taking art. And if half the students are taking art, then there are 64 students.
However, when I add up the ones not taking art, it comes out to 35. And 2/3 of 64 = 2/3(64) = 108/3 = 36. I can't get it to equal. I am sorry....I am not sure how to do this.

texaschic101 · Answer

@e.mccormick ...can you help...I am probably way off ??

texaschic101 · Answer

I a trying to figure out how any students in total. Is 64 correct ?

texaschic101 · Answer

typo...am

anonymous · Answer

@satellite73

texaschic101 · Answer

oohhh...get satellite...good idea....he is good

e.mccormick · Answer

The problem I see in even looking tat the table is in the very question.  "Find the probability that a student a Greendale middle school takes both art and spanish"  That has nothing to do with the table and just the numbers.  It is a probability of two simultaneous events.

texaschic101 · Answer

I see what you mean...I am confused

e.mccormick · Answer

Yes, and what I recall about doing that gives me none of the shown answers.

texaschic101 · Answer

we need to find the total number of students. And by going by the table, 32 take art. And if 1/2 of students take art, wouldn't there be 64 students ?

e.mccormick · Answer

The probability of the simultaneous occurrences of two independent events is the product of the probabilities of each event.  Takes Spanish is 2/3, art is 1/2.  $$\frac{1}{2}\cdot \frac{2}{3}=\frac{1}{3}$$ and for not Spanish it is 1/3, Not art 1/2:$$\frac{1}{2}\cdot \frac{1}{3}=\frac{1}{6}$$

texaschic101 · Answer

and according to the table, 35 do not take art....are we to assume that if they don't take art, they take spanish ?

texaschic101 · Answer

2/3 takes spanish....and if there is 64 students, 2/3 (64) does not equal 35...it equals 108/3 = 36. This is where I get lost.

e.mccormick · Answer

You are putting too much onto the table. The table looks to be a simulation result, which may or may not match the school. Take a look at this for the underlying math: http://www.mathsisfun.com/data/probability-events-independent.html

texaschic101 · Answer

But how are we to find the total number of students.....don't we need that

texaschic101 · Answer

1/2 take art......1/2 don't
2/3 take spanish....1/3 don't

e.mccormick · Answer

Not for the probability.  Not when you are given ratios.  If we needed to find the ratios, yes.But they were given, so that step is skipped.

texaschic101 · Answer

question....if they don't take art, do they take spanish ?
If 1/2 take art, that means 1/2 takes something else....can't be just spanish because 2/3 take spanish.

e.mccormick · Answer

Different classes at a different time of day.  Thus, independent events.

texaschic101 · Answer

I can't help her with this....maybe you can...you seem to know ore about this stuff then me

texaschic101 · Answer

typo....more

e.mccormick · Answer

Say they teach German, French, and Spanish.  And you are required to take 1 of the 3.  2/3rds are taking Spanish and 1/3rd are taking some combination of the other two.  Then say you must take art or music, 1/2 in art, 1/2 in music.  There would be other classes as well.  None of the rest matters because all this is looking at is just two independent classes.

My only problem with all of this was the:

3/20 2/5 7/20 1/10 

None of those would be related to the basic probability.  They might be related to the results of the table, which would be an evaluation of the simulation, and not the probability.

loser66 · Answer

I am with e.mccormick. My result is not one of her options.