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These events are not independent because it is more likely that it will rain in Galveston on days it rains in Houston than on days it does not.

The probability that a head comes up on the second toss is 1/2 regardless of whether or not a head came up on the first toss, so these events are independent.

You draw a card from a deck, then draw a second card without replacing the first.

The two events (1) “It will rain tomorrow in Houston” and (2) “It will rain tomorrow in Galveston” (a city near Houston).

The two events are (1) first toss is a head and (2) second toss is a head. Independent events if the probability of Event B occurring is the same whether or not Event A occurs. The prior example was looking at two independent events. The sample space is the set of all possible simple events.

If we roll a standard 6-sided die, describe the sample space and some simple events.

The sample space is the set of all possible simple events.

A simple event is an event that cannot be broken down further.

An event is any particular outcome or group of outcomes.

The result of an experiment is called an outcome.

In probability, we look at the likelihood of different outcomes. If you roll a die, pick a card from deck of playing cards, or randomly select a person and observe their hair color, we are executing an experiment or procedure. Theoretical probability, which is defined as follows: Suppose there is a situation with n equally likely possible outcomes and that m of those n outcomes correspond to a particular event then the probability of that event is defined as.

We will return to the experimental and subjective probabilities from time to time, but in this course we will mostly be concerned with But this is just a guess, with no way to verify its accuracy, and depending upon how educated the educated guesser is, a subjective probability may not be worth very much. Since there are so many variables to take into account, someone familiar with baseball and with the two teams involved might make an educated guess that there is a 75% chance they will win the game that is, if the same two teams were to play each other repeatedly under identical conditions, the Mariners would win about three out of every four games.

If someone asked you the probability that the Seattle Mariners would win their next baseball game, it would be impossible to conduct an experiment where the same two teams played each other repeatedly, each time with the same starting lineup and starting pitchers, each starting at the same time of day on the same field under the precisely the same conditions. Subjective in nature, in other words an educated guess. When a weather reporter says “there is a 10% chance of rain tomorrow,” she is basing that on prior evidence that out of all days with similar weather patterns, it has rained on 1 out of 10 of those days. Suppose we flipped a coin over and over and over again and it came up heads about half of the time we would expect that in the future whenever we flipped the coin it would turn up heads about half of the time. One would beĮxperimental in nature, where we repeatedly conduct an experiment. There are several ways of viewing probability. The probability of a specified event is the chance or likelihood that it will occur.