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)
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