Mathematics literacy Grade 10 " Conditional Probability"

Introduction

Jason Darren Herbett

218023510

Introduction

Good morning Grade 10 today we are going to do conditional probability which is based on how to handle independent events. But events can also be "dependent" which means they can be affected by previous events. Independent events can be independent meaning each event is not affected by any other events .

Example of an Independent Event :Tossing a coin 

Each toss of a coin is a perfect isolated thing. What it did in the past will not affect the current toss. The chance is simply 1-in 2 ,or 50%,just like any toss of the coin .So each toss is an Independent Event.

Example of Dependent event : Marbles in a Bag 

2 blue and  3 red marbles are in a bag. What are the chances of getting a blue marble? The chances is 2 in 5 .But after taking one out the chances change. So the next time .If we got a red marble before, then the chance  of a bleu marble next  is 2 in 4 .If we got a blue marble before, then the chance of a blue marble next  is 1 in 4.

In this chapter ,you will also be looking at tree diagrams which is a wonderful way  to picture independent and dependent events.

How to draw the tree diagram 

Probability trees are useful for calculating combined probabilities for sequences of events. It helps you to map out the probabilities of many possibilities graphically, without the use of complicated probability formulas.

The video below is based on how to draw tree diagrams. Watch the video and go through the content to gain more knowledge on the topic and complete the task.

 

 

 

Task

Conditional Probability:  Task

 

1.    Thomas is playing tennis. If it is windy, the probability that he serves an ace is 0.1. If it is not windy the probability that he serves an ace is 0.25. The probability that it is windy is 0.3.                                           

 

a)    Draw a tree diagram to represent the data given above.                                                        (10 marks)                 

b)    Calculate the probability that Thomas serves an ace.                                                             (4 marks)

      

2.    George has a bag of marbles. There are 6 red and 4 white marbles. George takes out a marble at random and records its color. Without replacement, George takes out another marble, at random.

 

(a)  Complete the probability tree diagram.                                                                                      (10 marks)

 

(b)  Find the probability that the two marbles are the same color.                                                    (6 marks)

            

3.    Andy sometimes gets a lift to and from college. When he does not get a lift he walks. The probability that he gets a lift to college is 0·4. The probability that he walks home from college is 0·7.

 

Getting to college and getting home from college are independent events.

 

(a)   Draw a tree diagram.                                                                                                                  (10 marks)

 

 

    b) Calculate the probability that Andy gets a lift to college and walks home from college.             ( 5 marks)

    c) Calculate the probability that Andy does not get a lift to or from college.                                    (5  marks)

     

 

                                                                                                                                                          ( TOTAL 50 )

 

 

Process

Step 1:

  • Read through the introduction on independent and dependent events . 
  •  watch the video on how to draw a tree diagram

Step 2:

  • Do some exercises on independent and dependent events 
  • Go through the content
  • Practice how to draw a tree diagram

Step 3:

  • Complete the task on conditional probability
  • Answer the all the answer in the task
  •  Answers should be completed  on a clean page and scan or take a picture   of answers and then send to teacher.
  • Include name and surname   
  • Send the scanned pdf document  herbettjason@gmail.com
Evaluation

Question 1

a)  [10 marks]

b)  [4 marks]

 

Question 2

 a) [ 10marks]

b) [ 6 marks ] 

 

Question 3

 a)  [10 marks]

b) [5 marks ]

c) [ 5 marks]

Question 1 [14 marks]

Question 2 [16 marks]

Question 3 [20 marks]

Rubric 

Rubric on Conditional  probability

Identification of possible outcomes

An incomplete set of outcomes for simple problems.

Simple problems include experiments of one task with one set (one die, one spinner, choosing marbles from one sock).

Lists a complete set of outcomes for a one task one set experiment and sometimes lists a complete set of outcomes for a two task experiment (sum of two dies, sum of two spinners) with limited and unsystematic strategies.

Consistently lists the outcomes of a two task experiment using a partially generative strategy.

Uses a systematic generative strategy that enables a complete listing of the outcomes for multiple task cases.

Statements of probability

Makes predictive statements with wording of most and least likely for events with subjective reasoning.

Recognizes certain and impossible events.

Makes predictive statements with wording of most and least likely for events based on quantitative reasoning, but may revert to subjective reasoning.

Recognizes certain and impossible events.

Makes predictive statements with wording of most and least likely for events based on quantitative reasoning including situations involving noncontiguous outcomes.

Uses numbers informally to compare probabilities.

Distinguishes certain, impossible, and possible events, and justifies choice quantitatively.

Makes predictive statements with wording of most and least likely for events based on quantitative reasoning for single task experiments.

Assigns a numerical probability to an event as either a real probability or a form of odds.

Comparing probabilities

Compares probability of an event in two different sample spaces using subjective or numeric reasoning.

Can not distinguish "fair" probability situation from "unfair".

Makes probability comparisons on the basis of quantitative reasoning (may not quantify correctly and may have limitations where noncontiguous events are involved)

Begins to distinguish fair probability situations from unfair.

Makes probability comparisons on the basis of consistent quantitative reasoning.

Justifies with valid quantitative reasoning, but may have limitations when non - contiguous events are involved.

Distinguishes fair and unfair probability generators on the basis of valid numerical reasoning.

Assigns numerical probability measures and compares events.

Incorporates noncontiguous and contiguous outcomes in determining probabilities

Assigns equal numerical probabilities to equally likely events

Probability comparisons are the ordering of the possibility of events happening.

Identify conditional probability

Does not give a complete list of outcomes even if a complete list was given prior to the first trial.

Recognizes when certain impossible events arise in non replacement situations.

Recognizes probabilities of some events change in a non replacement situation (as marbles are taken from a sock and not replaced before next draw) however, recognition is incomplete and is usually limited to events that have previously happened.

Can determine changing probability measures in a non replacement event.

Recognizes that the probability of all events change in a non replacement event.

Assigns numerical probabilities in replacement and non replacement situations.

Distinguishes dependent and independent events.

Conditional probability is the possibility of an event based on certain conditions.

 

 

Conclusion

Conclusion

Once you are finished you will be able to:

• Learners needs to be able to understand conditional probability.

•  Learners need to be able to simplify dependent events and independent events.

• Learners need to be able to understand how a tree diagram works.

• Learners need to be able to use tree diagrams to solve problems.

 

 

 

Credits

Mathematical literacy  Grade10 -12 book.

Teacher Page

 

My  WebQuest was created  to guide students in their ability to  understand  dependent events and independent events when dealing with conditional probability.

Teacher details 

Mathematical literacy student at Cput.

218023510

Jason Darren Herbett

herbettjason@gmail.com