Harper MTH165 Homework Section 4.3 Latest 2020 MAY

MTH165 ELEMENTARY STATISTICS

Homework Section 4.3

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) …