Challenging Probability examples?

[kenhung123]

Is there any VCE examples you personally think is good?
Any type of probability related questions would be appreciated!

[brightsky]

Find the possibility that there would be more heads than tails when a fair coin is flipped 18 times.

[kenhung123]

0.5927?

[brightsky]

Don't think so...

[kenhung123]

n=18, p=0.5, x=10-18
so 0.4072?

[pooshwaltzer]

KH, you got it...here's a bit of proof

[kenhung123]

Haha, love your spreadsheets!

[brightsky]

Yep. You got it.

Next (perhaps well-known) problem:

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

Another:

In a certain game, a player needs 10 wins to win. There are only two people playing, player A and player B and the prize money is $100. However, midway through the game's procession, player A was notified of an unforeseen emergency and had to leave. At the time player A had 7 wins and player B had 8 wins. After, they decided to divide the prize money according to said scenario. How should they divide the $100 so that it is fair for both player A and player B?

[kenhung123]

1. 0.0022
2. This is too hard...you need to draw a tree diagram that contains all the possibilities that A and B can reach 10 right?

[kamil9876]

1)If a real number from [0,1] is chosen at random, what is the probability that it is rational? jk but interesting

2) Two students play a game based on the total roll of two standard dice.  Student A says that a 12 will be rolled first.  Student B says that two consecutive 7s will be rolled first.  The students keep rolling until one of them wins.  What is the probability that A will win?

[brightsky]

1. 0.0022
2. This is too hard...you need to draw a tree diagram that contains all the possibilities that A and B can reach 10 right?

The first one defies intuition. It is much larger.
You are on the right track for the second one.

[/0]

Three points A,B,C are selected at random on the circumference of a circle. Find the probability that the points lie on a semicircle.

[kyzoo]

IME, probability question are automatic once you've done enough; the harder questions are based on functions.

[TyErd]

how do you do the matching birthday question?

[akira88]

how do you do the matching birthday question?

I'm curious too, I would have done the same as kenhung...
I have a feeling there's something to that question though...