Friday, April 1, 2011
$100 iPad 2 - if you register for MobileMe
Tuesday, March 15, 2011
Monty Hall
Most people are aware of the Monty Hall game show.Here is a short description:
The host, Monty Hall, offers you a choice of three doors. Behind one is a car, behind the other two are goats. After you have chosen one door, he would open one of the other two doors behind which there is a goat. Now you have two choices. You can either stay with your initial pick or switch. You will get whatever is behind the door you select. Should you stay or switch?
Most people think it is indifferent. This means whether you stay or switch the probability you will get the car is the same. But, there is a problem.Your original selection was when there were two goats and a car. Now, one of the doors that has a goat is eliminated. It should be better to switch, right? How much better would it be? Will your probability of getting a car increase by switching? Here is a simple proof:
When you first picked a door, the Probability that it had the car is 1/3.
What happens after Monty opened another door that has the goat?
- The probability of the first door containing the car is 1/3. Hence the chances of you getting a car by staying with your original choice is only 33.33%.
- Note, that you will surely get a car either by staying or switching. This means that the P(getting the car by staying) + P(getting the car by switching) = 1.
Hence, the probability of getting the car by switching is 2/3.
You are absolutely better off switching (unless you are aiming for a goat).
The host, Monty Hall, offers you a choice of three doors. Behind one is a car, behind the other two are goats. After you have chosen one door, he would open one of the other two doors behind which there is a goat. Now you have two choices. You can either stay with your initial pick or switch. You will get whatever is behind the door you select. Should you stay or switch?
Most people think it is indifferent. This means whether you stay or switch the probability you will get the car is the same. But, there is a problem.Your original selection was when there were two goats and a car. Now, one of the doors that has a goat is eliminated. It should be better to switch, right? How much better would it be? Will your probability of getting a car increase by switching? Here is a simple proof:
When you first picked a door, the Probability that it had the car is 1/3.
What happens after Monty opened another door that has the goat?
- The probability of the first door containing the car is 1/3. Hence the chances of you getting a car by staying with your original choice is only 33.33%.
- Note, that you will surely get a car either by staying or switching. This means that the P(getting the car by staying) + P(getting the car by switching) = 1.
Hence, the probability of getting the car by switching is 2/3.
You are absolutely better off switching (unless you are aiming for a goat).
Thursday, April 1, 2010
Happy April Fools Day
$100 iPads at Apple Store tonight at 10:00 PM - first 100 people only
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