Two Jars and 100 marbles

kcams
Posers and Puzzles 29 Dec '04 12:36
1. 29 Dec '04 12:36
this is an easy one,

you have 2 jars &amp; 100 marbles, 50 red and 50 blue.

you have to place the marbles into the jars such that you maximise the likelihood that you pick out a red marble.

i can get almost 3/4 or 75% likelihood.
2. TheMaster37
Kupikupopo!
29 Dec '04 13:23
1 red marble in jar 1 and the rest in jar 2 gives about 3/4 chance...74/99 to be precise

put x red marbles in jar 1 along with y black ones.

With chance 1/2 you pick a marble from jar 1, with chance x/x+y this is a red marble.

With chance 1/2 you pick a marble from jar 2, with chance 50-x/100-x-y this is a red marble.

1/2*(x/x+y + 50-x/100-x-y) = ugly

I have not the time to write ugly out, to differentiate to x and y and to see of they happen to have a common zero.
3. 29 Dec '04 14:15
Originally posted by kcams
this is an easy one,

you have 2 jars & 100 marbles, 50 red and 50 blue.

you have to place the marbles into the jars such that you maximise the likelihood that you pick out a red marble.

i can get almost 3/4 or 75% likelihood.
The statement of your puzzle is incomplete. What , wherefrom and how do you pick out has to be specified.
4. AThousandYoung
30 Dec '04 04:00
Originally posted by kcams
this is an easy one,

you have 2 jars & 100 marbles, 50 red and 50 blue.

you have to place the marbles into the jars such that you maximise the likelihood that you pick out a red marble.

i can get almost 3/4 or 75% likelihood.
Place the red marbles into both jars. Give the blue marbles to the kid down the street. 100%.

Place 25 blue marbles into each jar. Carefully, without disturbing the jars, place 25 red marbles on top of the blue marbles. 100%.
5. 30 Dec '04 11:26
Originally posted by cheskmate
The statement of your puzzle is incomplete. What , wherefrom and how do you pick out has to be specified.
you pick the jar and marble at random.
6. flexmore
Quack Quack Quack !
30 Dec '04 11:37
Originally posted by kcams
this is an easy one,

you have 2 jars & 100 marbles, 50 red and 50 blue.

you have to place the marbles into the jars such that you maximise the likelihood that you pick out a red marble.

i can get almost 3/4 or 75% likelihood.
ðŸ˜•
7. 31 Dec '04 13:03
Originally posted by kcams
you pick the jar and marble at random.
put 1 red marble in one jar and put all the rest in the other. The probability of picking a red marble would be;
(1+49/50)/2 = 74.99%....This is the maximum that can be achieved.
8. 02 Jan '05 15:18
Originally posted by ranjan sinha
put 1 red marble in one jar and put all the rest in the other. The probability of picking a red marble would be;
(1+49/50)/2 = 74.99%....This is the maximum that can be achieved.

????????????
how?....
9. AThousandYoung
02 Jan '05 15:28
There's a 50% chance you'll pick the jar with the red marble. If you pick this jar, you'll definitely get a red marble. (1/2)

If you don't pick that jar, then you'll have a 49/100 chance of getting a red marble.

Therefore the chance of getting a red marble is 1/2 + 1/2 * 49/100 = 100/200 + 49/200 = 149/200.
10. 02 Jan '05 15:36
expression was to be(1+(49/100))/2
11. 03 Jan '05 07:471 edit
Originally posted by muktadir
The second box contains 99 marbles, out of which 49 are red. Hence actually it will obviously be -
(1+49/99)/2 = 74.99%...
12. AThousandYoung
03 Jan '05 09:05
Originally posted by coolwarrior
The second box contains 99 marbles, out of which 49 are red. Hence actually it will obviously be -
(1+49/99)/2 = 74.99%...
Oops
13. 03 Jan '05 09:52
Originally posted by muktadir
It was a case of error due to hurried thinking and typing. Coolwarrior has already posted the correct expression. Thankx.
14. TheMaster37
Kupikupopo!
12 Jan '05 19:23
Originally posted by ranjan sinha
It was a case of error due to hurried thinking and typing. Coolwarrior has already posted the correct expression. Thankx.
*cough* In my days we were taught to simplify expressions like that.

Correct me if i'm wrong but it's not 74.99%

My calculation say it's 74/99 = 74.74 % approximately.
15. 13 Jan '05 11:03
Originally posted by TheMaster37
*cough* In my days we were taught to simplify expressions like that.

Correct me if i'm wrong but it's not 74.99%

My calculation say it's 74/99 = 74.74 % approximately.
put x = 1, and y = 0, in the expression (=ugly) given in your earlier post.