AP Test Review #3 Focus Binomial and Geometric Distributions Basic Probability Tree Diagrams.
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Transcript of AP Test Review #3 Focus Binomial and Geometric Distributions Basic Probability Tree Diagrams.
![Page 1: AP Test Review #3 Focus Binomial and Geometric Distributions Basic Probability Tree Diagrams.](https://reader035.fdocuments.in/reader035/viewer/2022071806/56649d0c5503460f949e0229/html5/thumbnails/1.jpg)
AP Test Review #3
Focus Binomial and Geometric Distributions Basic Probability Tree Diagrams
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Bernoulli Trial
A distribution where: The outcomes are success or failure Each trial is independent The probability of success is constant
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Binomial and Geometric Distributions
Binomial and geometric distributions are Bernoulli trials
Binomial Dist. – the probability of a certain number of successes out of a set number of trials (n,p,k)
Geometric Dist. – the probability that the 1st success occurs on the kth try. (p,k)
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Binomial Formulas
Probability of k success out of n trials (pdf)
Probability of k or fewer successes out of n trials – use binomial cdf!
Mean:
Standard Deviation:
knk ppk
n
)1(
npq
np
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Geometric Formulas
Probability of 1st success on the kth trial
Cdf = probability of 1st success occurs on or before the kth trial
Mean:
pp k 11
p
1
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Example 1:Assume the probability of getting a blue token
on each turn in a certain game is constant and equal to 0.35. Find:
a) The probability of getting 4 blue tokens in 7 turns.
b) The probability of getting at least 4 blue tokens in 7 turns.
c) Mean and standard deviation for the number of blue tokens in 11 turns.
d) The probability the 1st blue token occurs on the 5th turn.
e) The probability that it takes less than 4 turns to get the 1st blue token
f) The mean number of turns to get the 1st blue token.
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Answers
a) P = .14424b) P = .19985c = 3.85 and = 1.58193d) P = .06248e) P = .7254f = 2.857
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Basic Probability formulas
)(1)(
)(
)(
)()()()(
APAP
AP
BApABP
BAPBPAPBAP
c
Union (or)
Conditional (limit the total)
Complement
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Example 2The probability of going to the junior Prom is
47% and the probability of going to the senior Ball is 39%. In addition, the probability of going to both the Junior Prom and Senior Ball is 18%. Find
a) P(junior prom or senior ball)b) P(junior prom|senior ball)c) P(not going junior prom nor senior ball)d) P(going to senior ball but not junior prom)e) P(senior ball|junior ball)
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Answers
a) .47 + .39 - .18 = .69b) .18/.39 = .462c) 1 - .69d) .39 - .18 = .21e) .18/.47 = .383
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Last Example
The probability that a Freshman entering college goes straight to a 4-year school is 38%. The probability that a student that goes straight to a 4-year school graduating in 4 years is 27%. A Freshman entering college that goes to a 2-year school to start and graduating in 4 years is 19%.
a) Find the probability of graduating in 4 years.
b) Find the probability of a student starting at a 2-year college and graduating in 4 years.