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#126 Re: Help Me ! » Linear Programming and probabilty » 2009-07-05 22:36:16
For #1.
Let x = # of fender bolts per hour.
Let y = # of bumper bolts per hour.
So the constraints are
The feasible region has 5 corners and they are (0,0) (0,120) (110,120) (130, 100) (130,0)
#127 Re: Help Me ! » This can't be true! » 2009-07-05 10:49:13
Here's a useful purpose for the fact that 0.999.....=1.
I was at the casino looking at the Big Six wheel, there are 54 slots with 2 of them taken up by twenties which pay off at 20 to 1. What is the casino's advantage at this bet?
Well, since you don't lose your original bet when you win, you simply add 1 to the payoff, multiply the payoff times the probability and subtract from 1 to get the casinos advantage.
So, 21*(1/27) = 7/9 = 0.777777777...
We want to subtract this from 1 so 0.9999999... - 0.777777..... = 0.22222.....= 2/9
So the casino's advantage is a whopping 22.222...%. Horrible bet!
In this case, using the fact that 0.99999... = 1 makes things easier.
#128 Re: Jai Ganesh's Puzzles » *** Problems » 2009-06-17 13:14:11
Thank you for the interesting and challenging puzzles Ganesh.
#129 Dark Discussions at Cafe Infinity » Betelgeuse is shrinking! » 2009-06-11 11:24:18
- Fruityloop
- Replies: 14
http://news.aol.com/article/shrinking-s … r%2F521840
I thought this is interesting, Betelgeuse has shrunk by 15% over the last 15 years.
Which is the blink of an eye on cosmological time scales.
#130 Re: Exercises » Logarithms » 2009-05-31 21:02:23
The answer to #1.
We have
We set p equal to it and take the log of both sides
log p = log (
)log p =
log p =
log p = 0
p = 1:)
#131 Re: Exercises » Basic Probability » 2009-05-28 13:44:20
1. True
2. False
3. True
4. .1
5. .3
6. .3
7. .3
8. .4
9. .6
10. .7
#132 Re: Dark Discussions at Cafe Infinity » Unbelievable run at c r a p s... » 2009-05-25 11:39:03
Let us pretend that the population of the entire world (7,000,000,000) makes one attempt
every second for the entire history of the universe (4.32 x 10^17).
We have
So the probability of success is or
Which is 1 in
The actual probability will be lower than this because I'm assuming sampling without replacement.
I can only conclude one of two things:
1) She didn't really win 154 times in a row.
or
2) She cheated.
#133 Dark Discussions at Cafe Infinity » Unbelievable run at c r a p s... » 2009-05-25 01:09:31
- Fruityloop
- Replies: 1
http://www.app.com/article/20090524/NEW … 5/1001/rss
When she eventually "sevened out" around 12:31 a.m., after 154 rolls of the dice, she was greeted by Borgata with a champagne toast.
The odds of winning on each roll is .4929
So the odds of 154 winning rolls before finally losing is 1 in
Holy smoke!!!
#134 Re: Exercises » the remainder » 2009-05-19 01:15:15
Ok. I was trying to remove the highest power of 7 in the binomial expansion, (7^83). Instead of 7*83 which is the lowest odd power of 7 remaining. In the answer you don't have to worry about the second part of the sum because it is a multiple of 49. Very good. I think I finally understand.
Fruityloop.
#135 Re: Exercises » the remainder » 2009-05-18 23:07:37
JaneFairfax,
How did you go from
to
Thank You.
Fruityloop.
#136 Introductions » Hello everybody! » 2009-05-18 22:14:12
- Fruityloop
- Replies: 6
Hello everyone! I've just joined and I enjoy doing math in my spare time. I've been looking at some of the problems that people have posted and worked out. Some of the people on this forum are amazing! I hope to learn with everybody else on here. Cheers!