# E-Math: Interesting Probability Math Teaser (Plus usage of Tree Diagram)

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.

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### Ai Ling Ong

Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)

### 7 Responses to E-Math: Interesting Probability Math Teaser (Plus usage of Tree Diagram)

1. meera says:

> 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

2. kevin says:

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.

3. Mark says:

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)

i believe you're right

Sorry... mistake found. P(white marble) = 0.5 +(0.5 * 49/99)