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E-Math: Interesting Probability Math Teaser (Plus usage of Tree Diagram)
7 Comments · Posted by alwaysLovely in E-Math
You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, “Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK… you will die.”
How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?
Do you know how? ;) Leave your answer in the comment section. I will reveal the answer if anyone is interested to know.
In E-Math, we discussed about probability on possibility diagram, tree diagram, mutually exclusive events, independent events. Fortunately we do not go into permutation and combination where things get slightly more exciting.
Do you use more of tree or possibility diagram to help you in your probability question?
I’m going to show you an example of modified tree diagram to solve the following question
Bag A contains 15 bronze rings, 6 silver rings and 4 gold rings. Three rings are drawn at random, one after the other without replacement from bag A.
Calculate the probability of not drawing any gold ring.
Additional question: Calculate the probability of drawing all three rings that are different.
7 comments
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meera · January 7, 2010 at 11:07 am
> if he doesn’t mix the marbles and just puts white in one bowl and black in the other, the probability of getting white marble is 0.5 depending on the selectin of bowl.
> if he mixes evenly i.e., each bowl with 25 black and 25 white, the prob(white marble) is still 0.5.
regards
meera
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kevin · January 7, 2010 at 11:36 am
I dont really agree with Meera..remember a bowl will be chosen at random….If u use your method and the bowl with all black are chosen ur probabilty of living will be zero.
If u mix it gives you an even chance of living or dying from any bowl.
but then at the end of the day..it really would b ethe same,,,,U have a point…Now I see.
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Mark · January 7, 2010 at 11:16 pm
Put a white marble in one bowl and the rest of the 99 marbles in another bowl. Since you are blind-folded, the probability of choosing the bowl with the one white marble is 0.5. So P(white marble) = 0.5 +(49/99)
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OJY Reply:
January 13th, 2010 at 5:04 pm
i believe you’re right
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Mark Reply:
January 15th, 2010 at 8:49 am
Sorry… mistake found. P(white marble) = 0.5 +(0.5 * 49/99)
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alwaysLovely Reply:
January 19th, 2010 at 10:58 pm
Thank you for your participation!
Spot on!
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osamah · April 23, 2010 at 1:47 am
he should put 25 black and 25 white marbles in one bowl and do the same with the other one. now the probability of picking a white marble is 0.5 in both bowls and it doesn’t matter which bowl comes because probability of white marbles in both is equal.
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