November 2024
Problem of the Month

Urim and Thummim
idea from Janet S. Milton in the Mathematics Teacher



In Biblical times, the primary function of the priests was that of divining the will of God by the use of "Urim and Thummim."   The sacred container used for divining Urim and Thummim was a small box.   "Yes-no" type questions were brought to the priest.

He would place six stones, three white and three black, in the sacred container.
The black stones might represent "no" and the white, "yes."
The stones were mixed and three drawn at random.   If all three were white then God's answer to the question was "yes"; three blacks implied a "no" answer; and a mix indicated that God gave no response that day.

What is the probability of getting a "yes" answer to a given question?
What is the probability of God not answering on that day?

Click here for a more detailed explanation of the Urim and Thummim.



Solution:

The probability of getting a "yes" answer is 1/20.
The probability of not getting an answer is 18/20.

The probability is calculated easily with classical probability and the combinations formula for counting.   The experiment consists of selecting three stones at random from a collection of size six.
This can be done in 6C3 = (6!) / (3!3!) = 20 ways.

To get a "yes" answer, all three stones must be white.   This result can happen in only one way.   Thus, the probability of obtaining a "yes" answer to a particular question on a given day is 1/20.   Due to the symmetry of the system, the probability of a "no" answer is also 1/20; the probability that God would not respond is 18/20.



Correctly solved by:

1. Kamal Lohia Holy Angel School,
Hisar, Haryana, India
2. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
3. Davit Banana Istanbul, Turkey
4. K. Sengupta Calcutta, India
5. Colin (Yowie) Bowey Beechworth, Victoria, Australia
6. Kelly Stubblefield Mobile, Alabama, USA


Send any comments or questions to: David Pleacher