ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: kenhung123 on September 03, 2010, 05:16:05 pm
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Is there any VCE examples you personally think is good?
Any type of probability related questions would be appreciated!
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Find the possibility that there would be more heads than tails when a fair coin is flipped 18 times.
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0.5927?
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Don't think so...
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n=18, p=0.5, x=10-18
so 0.4072?
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KH, you got it...here's a bit of proof
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Haha, love your spreadsheets!
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Yep. You got it. :D
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?
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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?
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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?
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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. :)
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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.
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IME, probability question are automatic once you've done enough; the harder questions are based on functions.
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how do you do the matching birthday question?
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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...
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Find the probability that in a class of 25 students, there is at least two matching birthdays.
0.5678?
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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?
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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...
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whats the actual working out for it?
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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
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whats the actual working out for it?
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Yea, is this not binomial? :S
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whats the actual working out for it?
Wiki has a fairly good explanation of it: http://en.wikipedia.org/wiki/Birthday_problem
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ooo I didn't notice this thread, let's see... some of my fave probability paradoxes :P 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? :P
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Can someone help me out on part d of this question, is this a binomial?
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still don't understand how to do the birthday question
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what would the probability be of at least 2 people from 30 sharing the same birthday?
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ooo I didn't notice this thread, let's see... some of my fave probability paradoxes :P 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? :P
What if i choose B and be lucky enough to roll all 9's? Did you miss something?
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porbably something to do with the long run probability?
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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.
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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.
/looking further into it then the methods course
btw lol'd