## Teaser 2747: Marble jar

**From The Sunday Times, 17th May 2015** [link] [link]

At our local fete one of the games consisted of guessing the number of marbles in a jar: some of the marbles were red and the rest were blue. People had to guess how many there were of each colour.

The organiser gave me a couple of clues. Firstly, he told me that there were nearly four hundred marbles altogether. Secondly, he told me that if, when blindfolded, I removed four marbles from the jar, then the chance that they would all be red was exactly one in a four-figure number.

How many red marbles were there, and how many blue?

[teaser2747]

## Jim Randell 8:49 am

on29 September 2022 Permalink |If there are

Tmarbles in total (T= “nearly 400”) andRof them are red, then the probability of removing 4 red marbles is:And this probability is “one in a four-figure number”, so the largest it can be is 1/1000 and the smallest is 1/9999.

The following Python program considers total numbers of marbles from 399 down to 350, and then looks for numbers of red marbles that give an appropriate value for P.

It runs in 57ms. (Internal run time is 1.2ms).

Run:[ @replit ]Solution:There were 45 red marbles and 342 blue marbles.So, 387 marbles in total. And the probability of choosing 4 red is 1/6176.

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