Can Elementary Teachers Coach High School Sports

Locked in the attic

If you change the wording of a problem, it must be done taking into account the consequences. For example:

original Statement: In a house there are three key chains A, B and C, 5, 7 and 8 keys, respectively, of which only one in keychain opens the storeroom. A ring is chosen at random and it, wrench. Statement

changed: In a house there are three key chains A, B and C, 5, 7 and 8 keys, respectively, of which only one in keychain opens the storeroom. You take a random key.

The problem is, but let's stay with this part, which is important. Obviously, this problem is not the same take a key ring and then a random key that directly take a random key. Take a random key means that each key has 1 / 20 chances of being caught. As the shirts do not have all the same number of keys, so if you take a ring first and then a key, each key A is 1 / 15 chance of being, each key B, 1 / 21, and each key C, 1 / 24.

However, one can argue that if the keys are in key chains, it is impossible to pick up a key without taking prior to a keychain. This is what I defend my math teacher, who took the original problem of the book and changed the wording to put on the exam, thinking that addressing the problem would remain intact. And I say, okay, but if you take in the first instance of a keychain and then all of the key ring, key, why not take a random key.

Let's look at a Venn diagram:

L is superset of the sets A, B and C (key). If the statement says "pick a random key" is the same as "take a random element of L" . So, when choosing at random in the superset L, the sets A, B and C are not taken into account separately with equal probability.

But my teacher is in their heels. "If you put your hand to pick up a key, you must take before a key ring." Does it matter the fact of "putting your hand" if we are in math? Do not choose a random key numbering each and obtained by any method a random number from 1 to 20? I told him everything I have said here. Even I gave another example: If you have a ring with 99 keys and one with 1, choosing a random key, is the key which alone has 50% chance of leaving? To my surprise, I said yes.

In conclusion, he would not give me the reason why, in his opinion, by the fact that "you can not pick up a key at random without taking prior to a keychain," is the same as randomly choosing a key chain and then a key, to choose a random key. But no opinions, no objective evidence that is not equal. I think that my teacher understood me but would not budge.