finite math 1711 formulas and definitions

finite math topics: odd, probability using counting, conditional probability & independence, trees & baye's theorem, probability distributions, and binomial trials (bernoulli trials)

Odds

• if Pr(E)=a/a+b, then:

• Odds in favor of E are a to b, Odds against E are b to a

Unbiased Experiment

• Pr(E)=n(E)/n(S)=number of way E can occur/total number of possible outcomes

• Can incorporate combinatorics and set theory

Conditional Probability

• finding the probability of an event E given that event F has occurred

• Pr(E|F)=Pr(E∩F)/Pr(F)=Pr(both events E & F occur)/Pr(event that is given)

Independence

• E & F are independent if they have no effect on each other

• Pr(E|F)=Pr(E) and vice versa

• Testing for independence: Pr(E∩F)=Pr(E)xPr(F)

Difference Between Mutually Exclusive & Independence

Mutually Exclusive events cannot simultaneously occur, while independent events are when the occurrence of one event does not affect the occurrence of the other.

Trees

• Be able to draw tree from word problem, use to calculate other probabilities

Baye’s Theorem

• Pr(Ai)xPr(E|Ai)/Pr(A1)xPr(E|A1)+…+Pr(An)xPr(E|An)

• = product of numbers on branch through Ai and E/sum of products of numbers on all branches ending in E

Relative Frequency Distribution

• table that estimates the probability of each outcome based on frequency; used for experimental data

• determine this from chart & graph

Probability Distribution

• chart that lists all the outcomes in a sample space with their associated probabilities

• use different probability distributions to calculate probability of events

Random Variable

• rule that assigns a number to every outcome in the sample space; they’re usually denoted with X, Y, Z, etc.

Binomial Trials (Bernoulli Trials)

For an experiment to be a binomial trial:

1. experiment must be repeated several times

2. there are only 2 possible outcomes, success or failure

3. probabilities of success & failure do not change from trial to trial

4. each trial is independent of the previous trials

• Pr(X=k)=C(n,k)(p)^k(q)^n-k

• X is number of successes, n is number of trials, p is probability of success, q is probability of failure