# Independent probability

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Independent probability
Description
Exercise Name: Independent probability
Math Missions: High school statistics and probability Math Mission, Precalculus Math Mission, Mathematics III Math Mission
Types of Problems: 3

The Independent probability exercise appears under the High school statistics and probability Math Mission, Precalculus Math Mission and Mathematics III Math Mission. This exercise explores the multiplication rule for probability on independent events.

## Types of Problems

There are three types of problems in this exercise:

1. Multiple trials: This problem describes a situation where a trial is performed sequentially more than two times. The user is asked to find the probability of the experiment being successful on all trials, or being unsuccessful on all trials.
2. Two events: This problem describes a situation where two events are occurring simultaneously. The user is asked to find the probability that both, one of, or neither of the events are successful.
3. Known probabilities: This problem is also two events, like the previous problem, but this time the problem assumes basic knowledge of dice and coins. As before, the user is expected to provide the correct probability.

## Strategies

This exercise is medium to get accuracy badges because the event occurring versus the even not occurring can be subtle, so the problem needs to be read carefully. Speed badges should be considered hard until the timing tolerance is loosened to allow more time for careful reading when going quickly. They are, however, predictable as there is not much diversity among the problems at this time.

1. On Multiple trials the probability of success each time will generally be ${P^n}$ where as probability of failure each time will be ${(1-P)^n}$.
2. Multiple trials problems seem to be about free throws all the time for now.
3. Two events are always the captain and a pirate in sea battle for now.
4. Known probabilities are always a standard six-sided die roll and a two-sided coin flip.
5. Read carefully on problems to watch out for subtle uses of 'not' and the complement rule.

## Real-life Applications

1. Probability can be used to determine the chances of an event happening.
2. Data and statistics appear in news reports and in the media every day.
3. Many of the problems in this exercise could be viewed as real-life applications.
4. Statistics can be seen more frequently than calculus in every day life.