Backgammon Game
Question:

Consider throwing a coin multiple times. Even huge amount of times. Let's discuss - what would be the number of times you would get a particular side out of the total number of throws?

Let's see that in any occasion of throwing a symmetrical coin, the chance, or probability - that's the scientific name, of getting one particular side of the coin is one out of two options. That's 1 of 2, meaning probability of 1/2 to get a particular side.

Here is a video of throwing one Shekel coin multiple times. Please record the number of occasions that each side of the coin was visible.

 

Video source: original

What's the ratio of the number you've recorded to the total number of the results? How close is it to 1/2? What would it approximately be if we would throw the oin for 1,000 times?

It appears that the longer you throw and play with the coin, the closer the above ratio would be to the probability, which is 1/2.

 

Now you have a different story, please answer the following question:

Danny and Tali play backgammon.  They play for hours, making many throws of the two playing dice. If the total number of game turns was 360, what would be the approximate number of occasions that Danny and Tali saw six on both dice?

Backgammon
Source: Creative Commons licence, wikimedia.org

 

Watch also: MIT Blossoms video - The Monty Hall Problem or How to Outsmart a Game Show and Win a Car.

3 People tried to answer this question

36

5

10

60

Excellent job!

Explanation: probability to get 6 on both dice is 1/6 * 1/6 = 1/36. That is 10 out of 360.

Nice try, but that is wrong. That would be correct if there was one playing die.

Try thinking again.

Nice try, but that is wrong. Try reviewing the coin example again.

Nice try, but that is wrong. Try reviewing the coin example again.



Comments:
1.  Abu-Younis Ali Amona (16.06.2017 pm 07.14.20)
peer review
Generally, it is a good question. The question included most of the criteria for preparing a multi-choice question: background, original video, feedback for each distractor, and the question itself that ending in question mark. There is no reference  on the digital map, in other words the correlation to other phenomenon from everyday life is missing.  
Regarding the contents of:
1. Background: The background is short but lacking in scientific content and the aspect of statistical mathematical calculation. The background is presented as an example of a NISL injection and from there to calculate the probability.
2. The video is very nice,original, simple, short,interesting, clear and illustrates the subject of calculating probability. I like it. 
3. The responses to the distractors are also encouraging the questioner who made wrong answer, trying to solve again and get the correct answer. although, without prior knowledge of how to calculate probability, the question could not be solved correctly.
In summary, the question is good, clear, well organized, well formulated. Nevertheless, I would add a mathematical and statistical background, a link or links on the digital map to other phenomena in today's life, and making the question more challenging.

 



History of edits
Edited BY: Lior . Edit Date: 2017-06-15 09:13:06
Edited BY: Lior . Edit Date: 2017-06-15 09:12:21
Edited BY: Lior . Edit Date: 2017-05-23 23:15:58
Edited BY: Lior . Edit Date: 2017-05-23 23:12:51
Edited BY: Lior . Edit Date: 2017-05-23 23:05:39
Created By: Lior . Edit Date: 2017-05-23 23:04:24
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