# 3: Probability

- Page ID
- 22323

We see probabilities almost every day in our real lives. Most times you pick up the newspaper or read the news on the internet, you encounter probability. There is a 65% chance of rain today, or a pre-election poll shows that 52% of voters approve of a ballot of the ideas students think they know about probability are incorrect. This is one area of item, are examples of probabilities. Did you ever wonder why a flush beats a full house in poker? It’s because the probability of getting a flush is smaller than the probability of getting a full house. Probabilities can also be used to make business decisions, figure out insurance premiums, and determine the price of raffle tickets.

If an experiment has only three possible outcomes, does this mean that each outcome has a 1/3 chance of occurring? Many students who have not studied probability would answer yes. Unfortunately, they could be wrong. The answer depends on the experiment. Many math where their intuition is sometimes misleading. Students need to use experiments or mathematical formulas to calculate probabilities correctly.

- 3.3: Conditional Probabilities
- What do you think the probability is that a man is over six feet tall? If you knew that both his parents were tall would you change your estimate of the probability? A conditional probability is a probability that is based on some prior knowledge.

- 3.4: Expected Value and Law of Large Numbers
- Expected value is perhaps the most useful probability concept we will discuss. It has many applications, from insurance policies to making financial decisions, and it's one thing that the casinos and government agencies that run gambling operations and lotteries hope most people never learn about.

- 3.5: Counting Methods
- So far the problems we have looked at had rather small total number of outcomes. We could easily count the number of elements in the sample space. If there are a large number of elements in the sample space we can use counting techniques such as permutations or combinations to count them.