Question 194866:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! # 1
Remember, probability is simply a formal way of representing the chance of an event occurring. Probability is most often represented as a fraction where the numerator is the number of ways that given event can occur over the denominator which represents the total number of possible outcomes.
In other words, this fraction looks like
 = \frac{\text{Number of ways event can occur}}{\text{Total number of possible outcomes}})
where the notation "P(Event Occurring)" stands for "the probability of the event occurring"
So whenever you hear something like "the chances of that happening are one out of two", they mean that the event can occur one way out of two possible ways total. So they might be describing a coin toss where the chances of heads is "one out of two" since there's only one way to land on heads out of the two possible sides of the coin.
a)
Let's say that we have a deck of 52 cards and I want to know what the chances are of drawing a blue card. Since there are NO blue cards (there are only red and black cards), this means that the numerator is equal to zero while the denominator is still equal to 52. So this means that the probability of drawing a blue card is:
 = \frac{\text{Number of blue cards}}{\text{Total number of cards}}=\frac{0}{52}=0)
So the probability of choosing a blue card is 0 which means that there's a 0% chance of choosing a blue card.
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b)
Let's again say that we have a deck of 52 cards, but this time we want to know the chances of drawing a card (this is trivial, but important). Since there are 52 cards, and there are 52 ways to draw one card, this means that
 = \frac{\text{Number of ways to draw a card}}{\text{Total number of cards}}=\frac{52}{52}=1)
So the probability of drawing a card is 1. In other words, no matter which card you choose, you're still selecting a card. So there is a 100% certainty that you'll select a card.
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# 2
The outcomes of an experiment are the results after running the simulation. Whatever experiment you run, the outcomes are the OBSERVED occurrences of an event.
For instance, let's say that you're flipping a coin and you observe the coin lands on: heads, tails, heads, heads, heads, and tails.
The outcomes of the experiment are the results of heads, tails, heads, heads, heads, and tails where the experiment is flipping a coin.
Note: an experiment in this sense is simply a simulation of an event (eg flipping a coin, rolling a die, drawing a card)
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Here's another example. Now you're rolling a single die and you roll the following: 1, 4, 2, 5, 1, 6, 2, and 3
The numbers 1, 4, 2, 5, 1, 6, 2, and 3 are all outcomes of the experiment of rolling a die.
Note: A more sophisticated experiment would involve more factors (and not be as simple as rolling a die or flipping a coin).
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When we say that the outcomes are equally likely, we're simply saying that the probability of the outcomes are equal.
Back in the coin flipping example, the chances of landing on heads is  (since there's one way to get heads out of 2 possible outcomes). Likewise, the chances of getting tails is also (there's one way to get tails out of 2 possible outcomes).
Since  , this means that the chances of getting either one is equally likely. So this means that the outcomes are equally likely.
In the die rolling example, the chances of rolling any number from 1 to 6 are  (since for any given number, there's only one way to get that number out of the 6 numbers on the die). Since the chances of getting any number on the die is , these outcomes are also equally likely.
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