Identifying dependent and independent events

The first instance of  is under the Probability and statistics 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 student selects all of the multiple select options that pertain to the situation.Deind1.png
 * 2) Find probabilities then determine dependent or independent: This problem describes an experiment and two events. The student 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.Deind2.png

Strategies
This exercise is hard to get accuracy badges because the probabilities are becoming more intense at this stage. You will need to be very careful to ensure you 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 $$ P(A|B)=P(A), P(B|A)=P(B), P(A and B)=P(A) \times P(B) $$ so these will all be connected. In other words, if one holds they all do. If one doesn't, none of them will.