Challenging Probability examples?

[ttn]

Find the probability that in a class of 25 students, there is at least two matching birthdays.

0.5678?

[pooshwaltzer]

Find the probability that in a class of 25 students, there is at least two matching birthdays.

0.5678?

Spot on...as BrightSky will confirm.

How's about the prob when class size = say...100?

[ttn]

Find the probability that in a class of 25 students, there is at least two matching birthdays.

0.5678?

Spot on...as BrightSky will confirm.

How's about the prob when class size = say...100?

Surprisingly ~99.99%
Never would've guessed anything near that...

[TyErd]

whats the actual working out for it?

[pooshwaltzer]

Don't be surprised. This is how dating/matchmaking sites make their money. DoB is only one of the pertinent variables used to build correlations.

A slightly more bizarre question...

Andy tells the truth 55% of the time.
Brad tells the truth 90% of the time.
Corey tells the truth 33% of the time.

Dean, their teacher, asks his 3 students a simple question of "what's 1+1=?"

Andy will get the right answer 80% of the time.
Brad will get the right answer 50% of the time.
Corey will get the right answer 20% of the time.

The lights go out and somebody shouts an answer. Dean couldn't distinguish as to who had given the response.

QUESTIONS...
1. What is the probability that the CORRECT answer was shouted?

2. If the wrong answer was shouted, state the probability that it came from (i)Andy, (ii) Brad, (iii)Corey

[akira88]

whats the actual working out for it?

[kenhung123]

Yea, is this not binomial? :S

[ttn]

whats the actual working out for it?

Wiki has a fairly good explanation of it: http://en.wikipedia.org/wiki/Birthday_problem

[TrueTears]

ooo I didn't notice this thread, let's see... some of my fave probability paradoxes I was gonna post the birthday one as a starter but brightsky and pooshwaltzer both did it.

Here's one of my faves:

I invite you to a game involving 3 dice. The 3 dice are biased and have the following numbers on their faces:

DIE A: 3,3,5,5,7,7
DIE B: 2,2,4,4,9,9
DIE C: 1,1,6,6,8,8

You choose one of the dice, following this I choose another. Then we each roll our die 100 times and whoever scores more wins is the overall winner. The funny thing is, no matter how many times we repeat this, I will always win

Why?

Is there any way of beating me?

[kenhung123]

Can someone help me out on part d of this question, is this a binomial?

[TyErd]

still don't understand how to do the birthday question

[letsride]

what would the probability be of at least 2 people from 30 sharing the same birthday?

[kamil9876]

ooo I didn't notice this thread, let's see... some of my fave probability paradoxes I was gonna post the birthday one as a starter but brightsky and pooshwaltzer both did it.

Here's one of my faves:

I invite you to a game involving 3 dice. The 3 dice are biased and have the following numbers on their faces:

DIE A: 3,3,5,5,7,7
DIE B: 2,2,4,4,9,9
DIE C: 1,1,6,6,8,8

You choose one of the dice, following this I choose another. Then we each roll our die 100 times and whoever scores more wins is the overall winner. The funny thing is, no matter how many times we repeat this, I will always win

Why?

Is there any way of beating me?

What if i choose B and be lucky enough to roll all 9's? Did you miss something?

[kenhung123]

porbably something to do with the long run probability?

[/0]

All the die have the same expected value though.

But I guess if you have a die that has a 1 painted on one side and a 9 painted on the opposite side it will give a 1 more often since it takes more paint to paint a 9 so the 9 must be heavier.