Busy. Please wait.

show password
Forgot Password?

Don't have an account?  Sign up 

Username is available taken
show password


Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.
We do not share your email address with others. It is only used to allow you to reset your password. For details read our Privacy Policy and Terms of Service.

Already a StudyStack user? Log In

Reset Password
Enter the associated with your account, and we'll email you a link to reset your password.
Don't know
remaining cards
To flip the current card, click it or press the Spacebar key.  To move the current card to one of the three colored boxes, click on the box.  You may also press the UP ARROW key to move the card to the "Know" box, the DOWN ARROW key to move the card to the "Don't know" box, or the RIGHT ARROW key to move the card to the Remaining box.  You may also click on the card displayed in any of the three boxes to bring that card back to the center.

Pass complete!

"Know" box contains:
Time elapsed:
restart all cards
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

  Normal Size     Small Size show me how

Statistics 2

Probabilities, combinitorics, permutations

P(E) # of ways E can occur ______________________ total possible outcomes
Sample Space collection of all possible outcomes
Event a collection of outcomes
outcome any ONE thing that can happen
in a regular 52 card deck what is the probability of getting an ace? 4 ___ 52
Empirical Probability Counting observation, changes by observation # of times E occurred/ total # of observations
Contingency table make a grid to figure out the probabilities
The Law of Large Numbers (difference gets smaller w/ more observations) as you increase the number of observations the probability increases. P(|Pemp(E)-Pcl(E)|>S) -> 0
Make a list STAT ENTER
_ X Sample Mean
SX sample standard deviation
OX Population Standard Deviation
n Sample Size
Med Median (50% mark)
To compute 2 lists of descriptive stats STAT > ENTER enter data in list > STAT > CALC > > ENTER > 2ND > 1,2 (etc - use comma)
Permutation = NPR the number of ways to arrange r objects from a larger set of n objects. (one at a time) in a 52 card deck, how many ways to arrange?
Combination = NCR What is the probability of getting X from A any order?
Combination - What is the probability of getting a 5 card hand, all spades. 13 spades 13 c 5 cards ____________ 52 c 5 cards = 4.95 x 10-4
Permutation - In a 52 card deck how many 5 card hands are there? 52 c 5 = (math PRB NCR enter 5 enter)
n factorial The number of way to arrange n objects n MATH PRB ! ENTER ENTER
52 card deck arrange 7 cards on table, how many ways 52 P 7 = 52 MATH PRB NPR ENTER (52 npr) 7 ENTER
How many ways can you choose 5 people from a class of 50? 50 p 5 50 MATH PRB NPR ENTER (50 NPR) 5 ENTER
Complimentary Probability Given E, its opposite E is its compliment P(E) + P(E!)=1 so, P(E) = 1-P(E!)
Complimentary Prob - in a 52 card deck what is probability of getting one ace in 5 card hand? opposite of getting one ace is no ace = 1 - 48 C 5 / 52 C 5 (48 cards = 52 - aces - 1 ace in your hand)
Conditional probability Given 2 events (E given F) "Given a 52 card deck, what is the probability getting 5 spades, given all cards are black."
Given a 52 card deck, what is the probability getting 5 spades, given all cards are black P (5 spades/ black) #ways to get 5 spades # ways black 5 card hands spades 13 C 5 / 26 (black cards) C 5 = .0195
Independence (2 events) P(E given F) = P(E) Independent if proportion are the same dependent of proportions are not the same.
Are aces independent of hearts? P (ace/hearts) vs P(aces/cards) ace in hearts/# hearts = # aces /total # cards 1/13 = 4/52 (1/13) independent
Binomial Distribution (Bernouli) Roulette = Bernouli Poker blackjack = not bernouli Finite trials, 2 events (success vs fail), P(success) same from trial to trial, trials are independent
The probability of getting the flu is 18% Out of 10 friends, what is the probability of: between 2 and 4 get the flu P(X<n)=binom cdf (n [# of trials], p [probability of success],n [number of success])
What is the probability of sick at c- restaurant is 15%, out of 5 visits that you'll get sick twice? Note exact # (Binom pdf) 2nd VERS BINOMPDF (5,.15, 2) visits possible, %, sick actual
What is the probability of sick at c- restaurant is 15%, out of 5 visits that you'll get sick AT LEAST twice? Note range (Binom cdf) 1 - BINOMCDF (5, .15, 2) opposite of 2 or more - visits poss, %, top range - 1
Geometric Distribution: Basketball player has 54% free throw average. What is the probability he misses 4 and makes the 5th Note: Probability of 1st success on nth try 2nd VARS GEOMETCDF (.54, 5) (never pdf) probability, tries
If the probabilty of getting a role in a movie is 2.1%, what is the probability of getting it for the first time on the 1th try? 2nd VARS GEOMETPDF (.021, 10) = .0173
What is the probability of winning the lottery in your working lifetime: play once a week for 30 years 52 x 30 = 1560 times (3 steps incl. prob) 1/50 nCr 5 X 45 nCr 1 1 #/50 pos #s nCr 5# X 45 remaining # nCr 1 last # = 1.048 X 10-8 FINAL STEP: 1 - binompdf (1560, 1.05x10-8)
Given that the probability of being accepted by an ivy league school is 4.2%, what is the probability of: Getting in after 3 rejections? Specific # but no order GeometPDF (.042, 4) [after 3 means 4] .00369
Given that the probability of being accepted by an ivy league school is 4.2%, what is the probability of: getting in if you apply 4 times Exact # BinomPDF (4, .042, 1) = .1477 tries, %, success
The Poisson Distribution computing averages given data over time is used when: potentially infinite # of trials Trials are independent you have an average # of success per trial 4 errors/sec 5 strokes/ hole
Max safety level for ameb dysentary is 6 live org per liter. what is probability you get 7 live org? P(X) = Poisson PFD Exact P(<X) = Poisson CDF Range (7-1 = 6) 1 - PoissonCDF (6,6) = .3937 average,(7-1=6)
An internet service provider can handle up to 32 customers/sec what is the probability that any 5 sec intreval has at least 145 customers/ sec? Average # success - Poisson dist. 32 cust/sec x 5 sec = 160 AVERAGE MAX 1 - POISSONCDF (160, 144) = .8911 average, X (145 - 1 + 144)
Fatal auto accident rate in a suburb is 1/4500/year If the suburb has a population of 180,000 what is the probability of no more than 2 fatal accidents in a given year? 1/45,000 into 180,000 = 4 POISSONCDF (4,2) = .23810 average,X
Is the range open ended? (either end) Asking for probability? Draw out Graph, Mean is the center point NormalCDF continuous-U or L parameter is missing (10 99,L,M,O) (U,10 99,M,O) NORMALCDF (U, L, M, O)requires upper & lower Upper, Lower, Mean, Standard Deviation
Empirical Rule: Standard Normal Distribution
Created by: onesmartgirl