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

Normal Size Small Size show me how

# Statistics 2

### Probabilities, combinitorics, permutations

Question | Answer |
---|---|

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