Multiplying dependent probabilities

Multiplying dependent probabilities
Description
Exercise Name:	Multiplying dependent probabilities
Math Missions:	High school statistics and probability Math Mission
Types of Problems:	3

The Multiplying dependent probabilities exercise appears under the High school statistics and probability 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.

   

   Select what is true

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.

   

   Use diagram and find probabilities

3. Use formulas: This problem asks the student to find a particular probability based on the formulas for conditional and conjunctive probabilities.

   

   Use formulas

Strategies

This exercise is medium to get accuracy badges because there are a lot ways students 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 ${P(A\text{ and }B)=P(A)\times P(B|A)}$.
2. If students get that ${P(A \text{ and } B)=P(A)\times P(B)}$ then they know that the events are independent and vice versa.
3. It is always true that ${P(A \text{ and } B)=P(A)\times P(B|A)=P(B)\times P(A|B)}$

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.