Brain Teaser No 1

Alan,

I do hopeyou're not confusing pascal and fibonacci with yellow balls....

Cheers

Don

Minky,

Both balls are picked out at the same time.

and yes, the probability is one in three. Well done!

Now for the second part...

As your friend withdrew her hands from the sack with one ball in each hand, you noticed a glimpse of yellow between a couple of fingers of one hand.

What now is the probability of her having two yellow balls?

Cheers

Don

I guess that now the probability (because we already know that one of the balls is yellow) is one in two.

Before she draws we know that one of the balls will be yellow. Confirming it cannot improve our knowledge of what she has drawn.

Paul

I guess that now the probability (because we already know that one of the balls is yellow) is one in two.

Sorry Minky, this time Paul has got it right......but hey, ther'e always part 3...

Cheers

Don

Yellow balls - part 3

This time, you not only glimpse a bit of yellow between fingers, you actually see the number 1 on the ball.....

So now the probability of two yellows is......?

Cheers

Don

Pascal and Fibonacci,

I'm glad someone (Paul) liked it....i'll publish a more pragmatic version of Paul's explanation shortly....

Cheers

Don

So now the probability of two yellows is......?

Still hasn't changed.
John

Still hasn't changed.

John, I think this time it has......
Cheers

Don

Pascal et al...

starting with Pascal's triangle, i've shifted each successive row of numbers to the right so that each row starts one column to the right of the previous one.

I've then added up each column to give.......Fibonacci's series......

interesting (to a sad old git like me.....)

Cheers

Don

Taken from A Mathematician Plays the Market - John Allen Paulos


Early in the fall of 2002 Washington, D.C., sniper case, the police arrested a man who owned a white van, a number of rifles, and a manual for snipers. It was thought at the time that there was one sniper and that he owned all of these items. Given that there are about 4 million innocent people in the suburban Washington area, and one guilty person and police estimate that there are approximately ten people (including the guilty man) who own all three items. Which is higher:
a) the probability that an innocent man would own all these items?
b) the probability that a man who owned all of these items would be innocent?
John

John, I think this time it has......

Intuitively, the numbers on the balls is just spurious information that has no relevance. However, we have gone from a situation where the yellow balls are indistinguishable to one where they are. The drawing of two balls can now yield these three outcomes:

Yellow1 Red
Yellow2 Red
Yellow1 Yellow2

Fairly obviously if you can see the ball is yellow and number one, the combination highlighted is not possible. The probability would now appear to be 1 in 2, even though intuitively that feels totally wrong!
John

an innocent man

a) the probability that an innocent man would own all these items? must be about 9 in 4 million ie pretty low

and

b) the probability that a man who owned all of these items would be innocent? must be about 1in 10 ie pretty high


frightening.....but Mick Parry needn't worry......

Cheers

Don

[This message was edited by Don Atkinson on SATURDAY 08 November 2003 at 23:41.]

The probability would now appear to be 1 in 2, even though intuitively that feels totally wrong!

Ahh!!! the joy of probabilities.........

Cheers

Don

Why am I typing this at 9 p.m. on a Saturday? I'm off to the pub. It's ladies' night, and they are all seriously Alan-deprived.

brilliant idea.....six of us, including Mrs Don who is still my equivalent of 'its ladies night' have just got back from a fabulous evening at a nearby country pub that has just started a predominatly lebaneese menu.....where we particularly enjoyed the homos?.....homas?......humua?......oh, bugger it as our top man in waiting might say (allegedly) moi!

Cheers

Don

Don, it's "Hummus", with a heavy throaty "H".

well....my local Waitrose spells it Houmous....but I know what you mean about the deep throaty 'H'.....I worked in the Emirates (Trucial States), Oman and Saudi for 5 years....

Cheers

Don

I worked in the Emirates (Trucial States)

reminded me of my first tour to the 'Gulf' when I shared a 'portacabin' with an American pilot. The term 'Persian Gulf' had virtually changed to 'Arabian Gulf' and 'Persia' had become 'Iran'. He still got his mail delivered despite it being addressed to

Abu Dhabi
Trivial States
Persian Gulf

Cheers

Don

long time no visit... yeah, probability is fascinating. so, here goes:

its wimbledon 2004, and tim henman is in the final with andy roddick !!!

its the final set and tim is leading 5/3 !!!

the probability that either winning any of the following games is 0.5

(a) what is the probability that tim will win, without a harrowing tie break?

(b) what is the probability that tim will win, regardless

(c) what is the probability that this last set will go to a tie break?


we can only but dream, but here is a chance to put some numbers on your dreams...


enjoy

ken

I think that you don't get a tie break in the final set.

Paul

ken,

i have never understood the 'rules' of tennis scoring....sad, but true!! so i can't even begin to tackle this interesting probability teaser at present.

i believe that if tim wins the next game, he wins the set 6/3 (and the match), but i might be wrong on even this trivial point.

if tim doesn't win the next game, i believe he could still win 6/4 with the following game? otherwise the set (and match) is only won when one, or other, of the players gets two games ahead of the other, eg 7/5; 5/7; 8/6 etc (help!)

but i have never understood the 'tie-break' arrangement.....

i think the probability of me getting this one right looks like 0 at the moment!!

cheers

Don

i could pretend i wanted to test your knowledge of tennis, but i simply forgot about the tie break rule in composing this question. doh! so, yes, the probability is 0 for tie break. i simply changed the question to "final set" to introduce a bit of tension.

so, to make the question a little less exciting, lets just say winning the set, rather than the game.

in this case, omer's solution is correct.

end of dream.

enjoy

ken

but i simply forgot about the tie break rule

errrr.....so i still haven't found out what this rule is all about.......

cheers

Don

You have 2 Sticks........

I presume we are talking about 2 irregularshaped sticks that can't be marked with 1/4; 1/2; 3/4 length marks. In fact the only thing these two sticks have in common is that they burn for 1 hour???

cheers

Don

another one, nothing to do with tennis this time, in case i make another error in haste. this one had me bothered until i found a neat little trick.

x + y + z = 2

x^2 + y^2 + z^2 = 6

x^3 + y^3 + z^3 = 8

Bugger ! I was just listening to some music and the answer came to me. A negative number cubed is still a negative. Dah.