Show:
Independent v. Dependent v. Mutually exclusive
Conditional Probablity
Probability
Two-way table, Venn Diagram
Miscellaneous
100
What is the difference between independent and mutually exclusive?
Two events are independent if the occurrence of one event does not change the probability that the other event will happen. Two events are mutually exclusive if they have no outcomes in common and can never occur together. In other words independent events can occur together but never change the other, whereas mutually exclusive events can never occur together.
100
What is conditional probability and how is it denoted?
The probability that one event happens given another event is known to happen. It is denoted by P(B/A)
100
What is the definition of probability of a random phenomenon?
The proportion of times the outcome occurs in a very long series of repetitions.
100
For a Venn diagram, what goes in the intersection of the 2 circles?
A∩B
100
What does mutually exclusive mean?
When the two events have no common outcomes so they can never occur together.
200
What is the addition rule for mutually exclusive events?
P(A or B) = P(A) + P(B)
200
How do you find the probability that events A and B both occur? (Multiplication rule)
P(A∩B) = P(A) x P(B/A)
200
*look at table given on google docs* find P(home owner or high school grad)
P(home owner) + P(grad) - P(owner&grad) (340/500) + (310/500) - (221/500) = (429/500)
200
*look at table on google docs* find the missing values
liberal arts and A= 2142 engineering and below a B= 800 human services and B= 630 total A= 3392
200
What is the complement rule?
P(A^c) = 1- P(A)
300
Event A occurs with probability 0.8. Event B occurs with probability 0.2. If A and B are mutually exclusive then what does P(A or B) equal?
P(A or B) = P(A) + P(B) so... P(A or B)= 1
300
*look at graph on google doc* If you choose a student at random, what is the probability that they earned a Master's, given they were female?
P(masters/female) / (female) = 194/856 = .227 there is a 22.7% chance that a randomly chosen student earned their master's, given they're female.
300
The Pew Internet and American Life Project find that 93% of teenagers (ages 12-17) use the internet, and that 55% of online teens have posted a profile on a social-networking site. Find the probability that a randomly selected teen uses the internet and has posted a profile.
P(online & profile)= P(online)*P(profile/online) =0.93(.55) =0.5115 51.15% of teens use the internet and have a profile
300
*table will be on google doc* given the two way table, create a Venn diagram
*answer will be on board*
300
What is the law of large numbers? What does it mean?
It means if we observe more and more repetitions of any chance process, the proportions of times that specific outcome occurs approaches a single value. This value is called probability.
400
*look at table in google doc* Are the events "male" and "left-handed" independent?
P(left/male) = 7/47 = 0.152 P(left) = 10/100 = 0.1 0.152 does not = 0.1 These events are not independent
400
Your stats class has 19 students in it: 8 boys and 11 girls. Ms Feld uses a computer to select two students at random to solve a problem on the board. Given that the second student chosen is a boy, what is the probability that the first student was also a boy?
P(B1/B2) =P(B1∩B2)/P(B2) =(8/19)(7/18) / (8/19)(7/18)+(11/19)(8/18) = 0.38
400
*look at graph on google doc* if you choose a student at random, what is the probability that they earned a Master's degree?
365/1626 = .224 there is a 22.4% chance that a randomly chosen student earned their Master's degree.
400
*look at table given in google doc* find P(landline and no cell phone) find P(landline and cell phone)
P(landline and no cell phone)= 0.09 P(landline and cell phone)= 0.51
400
Draw a venn diagram that models the situation: The events A and B are mutually exclusive and have no common outcomes.
*answer on board*
500
In baseball, a perfect game is when the pitcher doesn't allow any hitter to reach base in all nine innings. Historically, pitchers throw a perfect inning about 40% of the time. What is the probability that a pitcher throws nine perfect innings in a row, assuming the pitchers performance in an inning is independent of his performance in other innings?
P(perfect pitch)^9 = (.4)^9 = 0.00026 = .026%
500
(look at board) A^c = female B^c = not pierced Find P(B^c/A^c)
P(B^c/A^c) = (44/178) / (88/178) = (4/178)*(178/88) = 4/88
500
*look at graph on google doc* Find P(L) and P(L/E)
P(L) = 3656/10,000 P(L/E) = P(L∩E)
500
WHS surveys families of its students and determines the following: if a family is chosen a random, the probability that they own a sedan is 0.23, the probability that they own an SUV is 0.42, and the probability that they own both is 0.14. Create a two way table that summarizes the probabilities above.
*answer will be on the board*
500
What is Ms. Feld's least favorite holiday?
Halloween