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Identifying dependent and independent events
Description
Exercise Name: Identifying dependent and independent events
Math Missions: High school statistics and probability Math Mission
Types of Problems: 2

The Identifying dependent and independent events exercise appears under the High school statistics and probability Math Mission. This exercise helps to clarify the difference between dependent and independent events via technical definitions.

## Types of Problems

There are two types of problems in this exercise:

1. Figure out dependent or independent: This problem describes an experiment and two events. If needed the user selects all of the multiple select options that pertain to the situation
2. Find probabilities then determine dependent or independent: This problem describes an experiment and two events. The user is asked to find the probability of several events and use these to determine if the events are dependent. It can also be multiple select.

## Strategies

This exercise is hard to get accuracy badges because the probabilities are becoming more intense at this stage. users will need to be very careful to ensure they do not make a mistake on 100 in a row. Speed badges are hard also, because of the time that is required to be careful enough to get answers correct.

1. If events are independent, then ${P(A|B)=P(A), P(B|A)=P(B), P(A \text{ and } B)=P(A) \times P(B)}$ so these will all be connected. In other words, if one holds they all do. If one doesn't, none of them will.

## Real-life Applications

1. Probability, along with decimals, percents, and fractions are used to determine the probability of a basketball player making a shot.
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.
5. Sports: When a team has a coin toss before the game, they have a 50/50 chance of winning it: either heads or tails.
6. Board Games: If one are using a game spinner with four sections – red, blue, green and yellow – they have a 25 percent chance of landing on any one color.
7. Medical Decisions: If one is told they need surgery, they’ll want to know the success rate of the operation. Based upon the statistics, they can make an informed decision whether or not it’s a good choice for them.
8. Insurance Premiums: Car insurance companies look at one's age and driving record when deciding their premium rate. If they see they've had several accidents, the likelihood is that they might have another one. In that case, their rates will be higher than a safe driver's.
9. Life Expectancy: Life expectancy is based upon the number of years similar groups have lived in the past. These ages are used as guidelines by entities such as financial advisers to help clients prepare for their retirement years.
10. Casino Games: Casino owners aren’t in the business to lose money. The odds are in their favor. Gamblers play the games, in hopes of defying those odds. In the game of blackjack, a player has a 1 in 20 chance of getting 21, a "blackjack." The probability is 5 percent.
11. Weather: If one is planning an outdoor event such as a wedding, they’ll want to check the probability of rain. Meteorologists predict weather based upon patterns that have occurred in previous years. Temperatures and natural disasters such as tornadoes, floods and hurricanes factor into forecasts.