Al-Hilālī’s Bag of Ten Coins: A Mathematical Case Against Blind Chance

In his commentary on Kitāb al-Tawḥīd by Imām Muḥammad ibn ʿAbd al-Wahhāb, al-ʿAllāmah Muḥammad Taqī al-Dīn al-Hilālī recounts an episode from his own life and presents a simple mathematical argument against the claim that the universe came into existence by chance. Al-Hilālī – well known to English-speaking Muslims as the co-translator of the widely used Hilali-Khan translation of the Qurʾān – writes:

Al-Hilālī’s Account

When I returned to Morocco seeking stability after the first revolution in Iraq, and after witnessing there the oppression and bloodshed perpetrated by the communists without distinction, the administration of the magazine Daʿwat al-Ḥaqq invited me to publish articles in it, in order to rescue the youth – and some older readers besides – from the confusion into which they had fallen regarding matters of creed.

I therefore turned to the book Man Does Not Stand Alone, written by the scientist Dr Cressy Morrison, formerly president of a scientific academy in the United States.I translated it into Arabic, supplied explanatory notes, and added my own comments throughout. The work was subsequently published in twenty-four instalments in Daʿwat al-Ḥaqq.

Here I shall present a single proof from the book, the very proof with which the author opens his introduction. Readers are encouraged to consult the work itself, whether in the English original or in my Arabic translation, the latter printed in Beirut under the title The Road to Allah. The example runs as follows.

Morrison’s Illustration

The author begins:

Suppose you take ten coins and write upon each one a number, from one to ten. Place the ten coins in a bag, then shake the bag vigorously until the coins are thoroughly mixed.

Now suppose you wish the coins to emerge in a fixed order: the first time you reach into the bag, you draw the coin marked “1”; the second time, the coin marked “2”; the third time, the coin marked “3”; and so on, until the last coin emerges precisely in sequence.

What would be your chance of drawing the coin numbered one on the very first attempt? One in ten.

On the second attempt, the chance of drawing the coin numbered two, having already drawn the coin numbered one, falls to one in a hundred.

Were you to reach into the bag three consecutive times and draw, in order, the coins numbered one, two, and three, your chance of success would be one in a thousand.

Were the first four coins required to emerge in sequence, the chance would fall to one in ten thousand.

Carried forward to the tenth coin, the probability that your hand would draw the coins numbered one through ten in their exact, ascending order reaches a figure beyond ordinary comprehension: one chance in ten million.

Al-Hilālī’s Conclusion

The purpose of this simple illustration is to render comprehensible the impossibility of the claim advanced by those who assert that this universe came into being, and arranged itself, by mere chance.

The existence of life upon our earth requires the convergence of a precise set of conditions. From the standpoint of mathematical probability, it is impossible for all of these conditions to converge, in their required proportions, through blind chance alone, upon any earth, at any time. It follows of necessity that behind nature there stands a wise, directing Being.

Once this is understood – and it is the truth – one knows with certainty that this universe was created with intention and deliberation, and that its existence was determined by precise measure before it ever came into being:

وَخَلَقَ كُلَّ شَىْءٍ فَقَدَّرَهُۥ تَقْدِيرًا ۞

“And He has created (every) thing, and has measured it exactly according to its due measurements.” (Qurʾān 25:2)

Reference

Al-Hilālī, M.T. al-Dīn (1407 AH). Sharḥ Kitāb al-Tawḥīd alladhī huwa Ḥaqq Allāh ʿalā al-ʿAbīd [Commentary on the Book of Tawḥīd, Which Is the Right of Allah upon His Servants], by Muḥammad ibn ʿAbd al-Wahhāb (d. 1206 AH). Edited by Abū ʿUbaydah Mashhūr ibn Ḥasan Āl Salmān. Riyadh: Dār al-Imām Muslim / Markaz Sutūr al-Baḥth al-ʿIlmī, p. 134.