The notation for conditional probabilities is

In this section you learned the basics of probability.

 

Looking at page 130 in your book, fill in the following:  ___ ______________________________ are probabilities calculated after information is given.  This is where you want to find the probability of ___________________ event A happening after you know that event B has happened

 

The notation for conditional probabilities is _ P(A,given B) _= P(A?B)

 

 ____________________.  The event following the vertical line is always ________________________the restricted sample space____________.  In other words, we can assume whatever is after the vertical line has already happened.

 

                Looking at page 131 in your book, fill in the following:  Events A and B are considered independent events if the fact that one event happens ____________ does not change the probability of the other event happening _____________________________________.

 

To check if events are independent we use the following:  A and B are independent if

 

_______ P(A?B)=P(A)______________ or __ P(B?A)=P(B)___________________

 

                What are the formulas for the two MultiplicationRules?

 

P(A and B) = P(A)*P(B)

 

P(A and B) = P(A)* P(B?A)

 

How do you know which one of the above formulas to use when you have to compute P(A and B)?

 

__________________________we use __ P(A and B) to calculate a conditional probability by using the restricted sample space and counting unless the sample space is large_____________________________________________

 

                For the exam, do you need to memorize all of the formulas above?  _yes_____

 

Why not? ___________________________________________________________________

 

Fill in the following as you work through your given problems in MyOpenMath.

 

1.            ____________________being prone to road rage_____________ and ___being in a car accident_________________________ (are/are not) independent     events because ___________________________________ the occurrence (or nonoccurrence) of one of them affects the probability of the occurrence of the other event.______________________________________

 

2.            _______________________losing your job__________ and ___selling your expensive car _________________________ (are/are not) independent      events because ______________________________________________ the occurrence (or nonoccurrence) of one of them affects the probability of the occurrence of the other event___________________________

 

3.            _______________________going to class__________ and ______passing the class______________________ (are/are not) independent          events because _________________________________ the occurrence (or nonoccurrence) of one of them affects the probability of the occurrence of the other event________________________________________

 

4.            _________________roads being icy________________ and ___being in a car accident_________________________ (are/are not) independent     events because ___________________________________________ the occurrence (or nonoccurrence) of one of them affects the probability of the occurrence of the other event______________________________

 

Remember that MATHENTERENTER will convert a decimal answer to a fraction.

 

5.            P(   all 7 of them are tails           ) = _____________________

 

                                                event                                                                    fraction                                                                                               

 

6.            P(   all of them are heads           ) = ______________________

 

                                                event                                                                    fraction

 

7.            P(    all 4 cards are kings          ) = ______________________

 

                                                event                                                                    fraction

 

8.            P(  all 3 cards are jacks            ) = ______________________

 

                                                event                                                                    fraction

 

9.            Fill in the following in the context of this problem:

 

                Individual:  a randomly selected _____the number of people who survived the Titanic_ _________based on class and gender_____________________________

 

                Variable 1:  ___ _________________________________________

 

                Type of variable:              qualitative                                           quantitative-discrete                                     quantitative-continuous

 

                Variable 2:  ____ ________________________________________

 

                Type of variable:              qualitative                                           quantitative-discrete                                     quantitative-continuous

 

                Use proper probability notation, fraction answer and rounded answer to 3 decimal places.

 

                a.            P(      M           ) = _________________________ ≈ ______

 

                b.            P(  1st class               ) = _________________________ ≈ ______________________

 

                c.             P(   M/1st class              ) = _________________________ ≈ ______________________

 

                d.            P(    M and 1st class             ) = _________________________ ≈ _______

 

                e.            P(    M or1st class             ) = _________________________ ≈ ________

 

                f.             _____________________ ____________ and _____ _______________________ (are/are not) mutually

 

                                exclusive because… P(male and 1st class) is not equal to 0

 

                g.            ________________________________ and ____________________________ (are/are not)

 

                                independent because (look at 4th bullet on front page) P(male | 1st class) is not equal to P(male) …

 

10.          Fill in the following in the context of this problem:

 

                Individual:  a randomly selected ______number of dolphins groups that were partaking in an activityat certain number of days______________________________________

 

                Variable 1:  _____________ _______________________________

 

                Type of variable:              qualitative                                           quantitative-discrete                                     quantitative-continuous

 

                Variable 2:  ____________ ________________________________

 

                Type of variable:              qualitative                                           quantitative-discrete                                     quantitative-continuous

 

                Use proper probability notation, fraction answer and rounded answer to 3 decimal places.

 

                a.            P(     dolphin group is partaking in travel                                                                 ) = _________________________ ≈ _____________

 

                b.            P(    dolphin group is around at noon                                                                       ) = _________________________ ≈ _______

 

                c.             P(   dolphin group is partaking in travel given that it is around at noon                                                                      ) = _________________________ ≈ __________________

 

                d.            P(dolphin group is around at noon given that it is partaking in travel) = _________________________ ≈ ______________________

 

                e.            P(  dolphin group is around in the morning given that it is partaking in social activities                                                                       ) = _________________________ ≈ _____________________

 

                f.             P(     dolphin group is around in the morning and is partaking in social activities                                                                    ) = ________________________ ≈ ______________________

 

                g.            P(     dolphin group is around in the morning or is partaking in social activities                                                                       ) = _________________________ ≈ ____ __________________

 

                h.            _____________ dolphin group around in the morning ____________________ and ___ dolphin group partaking in social activities _________________________ (are/are not) mutually

 

                exclusive because P(around in the morning and partaking in social activities) is not equal to 0 …

 

                i.              ________________ dolphin group around at noon _________________ and ___ dolphin group partaking in travel _________________________ (are/are not)

 

independent because (look at 4th bullet on front page) P(around at noon | partaking in travel) is not equal to P(around at noon)