Matthew is the ugliest guy in his school. Therefore, the probability that he can have a beautiful girlfriend is 0.001. Suppose he woos 10 beautiful girls at the same time. What is the probability that Matthew can have at least one beautiful girlfriend?

Question

parthkohli · Answer

1 - P(he can't have any girlfriend)...?

lgbasallote · Answer

and that would be...?

parthkohli · Answer

P(he can't have any girlfriend) = 1 - P(he can have all girlfriends) maybe.

lgbasallote · Answer

...you're just looping....

lgbasallote · Answer

my thoughts... $$\huge 1 -  _{10} C _0 \times (0.001)^0 \times (0.999)^{10}$$
but a part of me knows this is wrong...

terenzreignz · Answer

To be clear
Suppose he woos a girl, the odds that that girl becomes his girlfriend is 0.001 ?

lgbasallote · Answer

probability

terenzreignz · Answer

Then why can't it just be 10 x 0.001? after all, he does it ten times

lgbasallote · Answer

...because i don't think it's that simple...

zarkon · Answer

@terenzreignz 
what if it was 100,000 girls..what would the probability be then.

terenzreignz · Answer

Ok, that was a long shot, too good to be true :)

lgbasallote · Answer

so i assume you know how to do this @Zarkon ?

zarkon · Answer

yes

lgbasallote · Answer

am i right?

zarkon · Answer

provided you have some added assumptions...

lgbasallote · Answer

by that you mean...?

zarkon · Answer

the girls selected are independent from each other and that the .001 applies to all girls equally

zarkon · Answer

then this follows a binomial distribution

zarkon · Answer

and you are correct

lgbasallote · Answer

wonderful

lgbasallote · Answer

here's a question out of curiosity....how many girls should he woo to make sure that he can get one of the beautiful girls to be his girlfriend?

zarkon · Answer

infinite..otherwise there will be a positive probability that he will not get one

zarkon · Answer

if you want above a 50% chance then you would need 693

zarkon · Answer

above 90% you would need 2302

lgbasallote · Answer

is the above 50% the one where he can surely get one of the girls to be his girl?

zarkon · Answer

no

zarkon · Answer

half the time he still would not get one

lgbasallote · Answer

i think my question is related to that saying "In a group of 23, two of the people will surely have the same birthday" or something

zarkon · Answer

the only way to be 100% positive her would get a girl is to have an infinite number of girls to 'work' on

zarkon · Answer

for the b-day problem the 23 just gives you a slightly better than 50% chance of having a matching birthday.  It does not guarantee it

lgbasallote · Answer

ah yes. that was the saying

lgbasallote · Answer

is it related?

zarkon · Answer

no..for the b-day problem if you have more that 365 people then you will have at least one match

parthkohli · Answer

```
the only way to be 100% positive her would get a girl is to have an infinite number of
girls to 'work' on
```
That is more like the infinite monkey theorem!

lgbasallote · Answer

what about the 5% theorem thing? is it applicable?

zarkon · Answer

not sure what you are referring to

lgbasallote · Answer

http://en.wikipedia.org/wiki/P-value

zarkon · Answer

that is a stretch 'p-value' and '5% thing' ;)

zarkon · Answer

p-values are for hypothesis tests

lgbasallote · Answer

5% is a p-value that was what i was referring to

zarkon · Answer

this is not a hypothesis testing problem

lgbasallote · Answer

if the probability is less than 5% then it's significant...so i supose here we assume prob to be > 5%

lgbasallote · Answer

hmm so i suppose nothing fits huh

lgbasallote · Answer

matthew will have to take his chances

zarkon · Answer

"5% then it's significant." that depends on who you are asking and what is being tested

zarkon · Answer

for medical testing one usually goes much lower than 5%