Finite Mathematics.. easy question

[LuDaCriS66]

This is a pretty easy question but I need a solution for it... it involves combinations, inclusions and exclusions.. things like that

"A package of 20 transistors contains fifteen that are pefect and 5 that are defective. In how many ways can five of these transistors be selected so that at least 3 are perfect?"

Anything to do with the fundamental counting principle?

Another question:

"A survey of television viewers produces the following data:
60% watch X
50% watch Y
50% watch Z
30% watch both X and Y
20% watch both Y and Z
30% watch both X and Z
10% watch all three shows

a) what percentage view at least one of these programs?
b) what percentage view none of these shows?

if anyone can help, it'd be appreciated...

also if anyone knows of an online finite mathematics help site, please post the link..
anything like the www.ihatecalculus.com site would be great..

as u can see I'm not very good at math so I need this help thanks

 

[LuDaCriS66]

bump

 

[Shaftatplanetquake]

Damn those are hard questions. Can't help.

 

[b0mbrman]

Here's the way to do the first one...find the total number of combinations then *SUBTRACT* the probability that 3 are defective, 4 are defective, 5 are defective

 

[OREOSpeedwagon]

Ohh...my head...too...many numbers...

 

[LuDaCriS66]

<< Here's the way to do the first one...find the total number of combinations then *SUBTRACT* the probability that 3 are defective, 4 are defective, 5 are defective >>



Great! I forgot about that! Thanks

 

[bizmark]

Okay, so this seems really complicated, and I use a lot of notation to keep from having to type everything a million times, but it's really not that hard.



<< "A survey of television viewers produces the following data:
60% watch X
50% watch Y
50% watch Z
30% watch both X and Y
20% watch both Y and Z
30% watch both X and Z
10% watch all three shows

a) what percentage view at least one of these programs?
b) what percentage view none of these shows? >>



So we have 8 kinds of people:
A - watch X only
B - watch Y only
C - watch Z only
D - watch X and Y
E - watch X and Z
F - watch Y and Z
G - watch X, Y, and Z
H - watch none of X,Y,Z

Note that these are mutually exclusive classes. That's how we want it! You can draw a Venn diagram with three intersecting circles, each of which represents X, Y, and Z. The area in the middle is the 10% who watch X,Y,Z.

For simplicity let's just say that there's 100 people and then we can talk about numbers instead of percents.

We know already that there are 10 G people.
There are 30 people that watch both X and Y, but 10 of them also watch Z and are therefore G people. So the number of D people is 20.
There are 20 ppl that watch Y and Z, but 10 are G ppl and so we have 10 F ppl.
There are 30 ppl that watch X and Z, but 10 are G ppl and so we have 20 E ppl.
There are 50 ppl that watch Z, but 10 of them watch X and Y too (G ppl), and 10 of them also watch just Y (F ppl), and 20 of them also watch just X (E ppl), so we're left with 50-10-20-10=10 ppl who just watch Z (C ppl).
There are 50 ppl who watch Y, but 10 of them are G ppl, 10 of them are F ppl, and 20 of them are D ppl, so now we have 10 ppl who watch only Y (B ppl).
Lastly, there are 60 ppl who watch X, but 10 of them are G ppl, 20 of them are D ppl, and 20 of them are E ppl, so we have 10 A ppl.

So to sum that up:
10 watch only X
10 watch only Y
10 watch only Z
20 watch only X and Y
20 watch only X and Z
10 watch only Y and Z
10 watch X, Y, and Z
Sum this up to get 90, the amount of people who watch at least one show. The number of people who watch none of the shows is 100-90=10.

Would somebody mind checking that for me? my head is hurting now....

But I worked it out again on paper and got the same numbers. So I think that that's the right way to do it. As I said at the top, it could be a lot smaller with less notation, but since I'm typing this on a computer (no diagrams or anything) I wanted to keep everything straight. Also I wanted to give all of my reasoning so it had to be pretty long but by saying "similarly" or something it could've been a lot smaller. There were also a couple of shortcuts that I could've taken, but again, it's best to be as complete as possible.

 

[LuDaCriS66]

WOW! Thank you SO much! Your answers were 100% correct. I understand it completely too! Cool.. now I'm gonna ace this test tomorrow thanks to you guys.. hehe

again.. I can't thank you enough for all that work you put into it.. I really really appreciate it