Way back in my college days, I always feel excited every time I join engineering quiz competitions. I am also enjoying here in Steemit with the contests initiated by fellow Steemians. It feels me like I am still in college. The latest one I joined a big challenge was 
Somehow, I found Sir 
You are a prisoner sentenced to death. The King offers you a chance to live by playing a simple game.
He gives you 50 red marbles, 50 black 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 Red 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 Red Marble?
This is the simplest explanation. If the bowls are just to be switched or mixed without me knowing, then selecting a bowl and then a red marble at random is just the same selecting a red marble from a bowl containing 50 red and 50 black marbles.
Oh, you need a more complex explanation? Here it is!
There are two successive events and two mutually exclusive multiple events. The first event is to choose a bowl. So, the probability to have the first bowl is ½ and so for the other. The second event is choosing a red marble which depends upon how I placed the marbles into the bowls. But, these have another mutually exclusive event.
What are mutually exclusive events?
Mutually exclusive events are events that do not occur at the same time.
For example, I have to choose at random two marbles with the same color in a bowl that contains both 10 red and 20 black marbles. Then, the favorable events are: Red-Red or Blue-Blue. If choosing both red takes place, then blue-blue won’t happen any longer or if blue-blue take place, then red-red won’t happen anymore. But before any event has occurred, consider that all of them as favorable events.
By principle, the probabilities of mutually exclusive events must be added. So, suppose I am to place all the 50 red marbles in first bowl and 50 black in the second. Then the probability to get a red marble is:
P = ½(1) + ½(0)
P = ½
What if I’ll arrange them by 25-25 in each bowl? I mean, 25 blacks and 25 reds in one bowl and so as in the other. Then the probability is:
P = ½ (25/50) + ½ (25/50)
P = ½
Let’s try 10-40 and 40-10. Ten black and forty red marbles in the first bowl and 10 red and 40 black marbles in the second. Then the chance for you to get the red one is:
P = ½ (40/50) + ½ (10/50)
P = ½
All result is just ½ or 50%. I also made a calculation using an excel file to check the probability of each combination.
There are five people. One of them shot and killed one of the other five.
- Dan ran in the NY City marathon yesterday with one of the innocent men.
- Mike considered being a farmer before he moved to the city.
- Jeff is a topnotch computer consultant and wants to install Ben’s new computer next week.
- The murderer had his leg amputated last month.
- Ben met Jack for the first time six months ago.
- Jack has been in seclusion since the crime.
- Dan used to drink heavily.
- Ben and Jeff built their last computers together.
- The murderer is Jack’s brother. They grew up together in Seattle.
Sherwin Grey arrived at the scene and immediately finds the murderer.
Who was the murderer?
Dan absolutely isn’t the murderer, is he? Dan surely couldn’t run in the marathon if he is the killer who has an amputated leg.
Ben just met Jack six months ago. So obviously, he is not the killer who is Jack’s brother. Speaking of Jack. Jack is the brother of the murderer. So, for sure he is not his brother, is he? That’s why he’s been secluded after the crime.
While Mike., Oh Mike? Who is he by the way? A once farmer who moved to the city. But where is he now? Dan, Jeff, Ben, and Jack are very alive. This could only mean that Mike is the one that is murdered.
A man has to get a fox, a chicken, a sack of corn across a river. He has a rowboat, and it can only carry him and one other thing. If the fox and the chicken are left together, the fox will eat the chicken. If the chicken and the corn are left together, the chicken will eat the corn.
How does the man do it?
| No. | Left | Boat | Right |
|---|---|---|---|
| 0 | man, fox, chicken, corn | ||
| 1 | fox, corn | man & chicken ==> | |
| 2 | fox, corn | <== man | chicken |
| 3 | corn | man & fox ==> | chicken |
| 4 | corn | <== man & chicken | fox |
| 5 | chicken | man & corn ==> | fox |
| 6 | chicken | <== man | fox & corn |
| 7 | man & chicken==> | fox & corn |
| No. | Left | Boat | Right |
|---|---|---|---|
| 0 | man, fox, chicken, corn | ||
| 1 | fox, corn | man & chicken ==> | |
| 2 | fox, corn | <== man | chicken |
| 3 | fox | man & corn ==> | chicken |
| 4 | fox | <== man & chicken | corn |
| 5 | chicken | man & fox ==> | corn |
| 6 | chicken | <== man | fox & corn |
| 7 | man & chicken==> | fox & corn |
As you see, the events differ starting the third sail in choosing what to bring. Either the fox or the sack of corn.
If you haven't read the original post! See it here.
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