Multiplying dependent probabilities

The first instance of  is under the Probability and statistics Math Mission. This exercise practices formulas for multiplication and conditional probabilities.

Types of Problems
There are three types of problems in this exercise:


 * 1) Select what is true: This problem describes a situation and asks the student to select the answers from a list that are true statements.Multdepprob.png
 * 2) Use diagram and find probabilities: This problem has a diagram or chart drawn and asks the student to answer a sequence of questions about probability related to the situation.Multdepprob2.png
 * 3) Use formulas: This problem asks the student to find a particular probability based on the formulas for conditional and conjunctive probabilities.Multdepprob3.png

Strategies
This exercise is medium to get accuracy badges because there are a lot ways you can guarantee one true statement giving others. The speed badges are hard because the problems sometimes require a lot of thought to get correct.


 * 1) A useful formula that comes up is $$P(AandB)=P(A)\times P(B|A)$$.
 * 2) If you get that $$P(A and B)=P(A)\times P(B)$$ then you know that the events are independent and vice versa.
 * 3) It is always true that $$P(A and B)=P(A)\times P(B|A)=P(B)\times P(A|B)$$