Description of Activity/Phenomena:

Typical Observations:
    The more possible outcomes there are the less likely it is to win.
    The more opportunities there are to win, the more likely it is to win.
    Probability is defined as likelihood or chance for winning or something to occur.
    There are no guarantees to win or for something to occur unless there is only one choice.

Explanation:
    In the dictionary probability is defined as: 1. being probable, 2. something that is probable, 3. a ratio expressing the chances that a certain event will occur, and 4. a branch of mathematics studying chances of random events.  But what exactly does this mean? As can be seen from the activity, probability is the opportunity that a person (or thing) has to win or have something occur.  It is a chance.  People say that "You have a better chance of being hit by lighting than winning the lottery."  To make this statement, someone has calculated the probability that the set of numbers which you pick will be the winner compared with all the possible combinations of numbers that could be drawn as a winner, and then compared that ratio with the kid of ratio for getting struck by lighting.  Probability is likelihood.  The higher the probability for something to happen, the better the chances are; it is a good bet.  Compare winning with the coin and winning with the die.  You have a 1 in 2 chance of throwing a tail on the coin as compared to a 1 in 6 chance of throwing a three on the die.  The respective probabilities are .5 and .167 for each of the two scenarios.  If you were betting money on winning the game, which would you rather bet on? The Coin throw or the Die roll?  The coin throw of course because there is a greater likelihood of winning.  That is what probability does, it tells us how good the likelihood it.

    The probability can be affected by factors other than just the number of outcomes.  When comparing the probability of winning with the coin and the die, the probability of winning with the die is less because there are more possible outcomes which do not win when compared to the coin.  However, we can increase the probability of winning with the die if we allow two different numbers to be wins.  If you can win by rolling a three or a four, then the probability of winning has increase (from .167 to .333)- a better bet!  Another way to increase the probability is to "tilt the scales" or "weight the results." For example, if we weight the coin to fall towards the tails side (say by giving the heads side a little more weight so that if it lands directly on the edge of the coin will fall on the heads side), then the probability of use winning is no longer .5.  We have added some other factors to our game so that when we play the game again we will win 3 out of 4 times.  Weighting the coin increased our probability of winning (from .5 to .75).

     If something will be found in one place with a .25 probability and in another place with a .05 probability, then we would want to look at the first place to find the particle because it is more likely we will see it there than the other place.  We use this idea to define where electrons will be and form orbitals.  We find the probability that the electron will be in all the different positions in three-dimensional space (computers are almost always used to do these calculations) and then we draw a surface on which the probability of finding the electron on any point on that surface is 90%.  Now if someone is looking for an electron, they just have to look on this entire surface, and they will have a high likelihood of finding the electron.  Like weighting the coin or providing two different ways to win, there are factors effecting the probability of the electron's location.  The attraction between the protons and electrons weight the probability towards the nucleus of the atom.  The probability of finding the electron will be greater closer to the nucleus, so when calculating the probabilities to draw the 90% surface, this factor is take into consideration.  Another factor influencing the probability calculations is electron-electron repulsion.  An electron does not want to be near another electron so this will effect the probability like the attractions between the protons and electron but in the opposite manner.  The probability calculations are difficult to find the orbitals, but this activity provides a simplified idea of what is occurring; winning the game is like finding the electron.
 
 
 
 

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