COMBINED Probability Calculators RevA(1)

2 X 2 Contingency Tables for Probabilities us Event A Event B A B 0.5 Not B 0.17 Totals 0.67 Probabilities Calculations Simple Probabilities Event B P(B) = P(Not B) = Event A P(A) = P(Not A) = P(B and A) = P(B and Not A) = P(Not B and A) = P(Not B and Not A) = P(B or A) = P(B or Not A) = P(Not B or A) = P(Not B or Not A) = "Event A GIVEN Event B" P(B | A) = P(Not B | A) = P(B | Not A) = P(Not B | Not A) = Joint Probabilities ("A AND B") Addition Rule ("A OR B") Conditional Probabilities ("A GIVEN B" or "B GI

"Event B GIVEN Event A" P(A | B) = P(Not A | B) = P(A | Not B) = P(Not A | Not B) =

0.8772 0.1228 0.3953 0.6047

General Format When expressed in proportions (% Grand Total) Event B Yes No Total P(A) P(not A) P(B) P(not B) 1 General Format When expressed in counts Event B Yes No Total C(A) C(not A) C(B) C(not B) C(A∩not A) or C(B∩not B) P(A ∩ B) P(A ∩not B) P(not A ∩ B) P(not A ∩not B) C(A ∩ B) C(A ∩not B) C(not A ∩ B) C(not A ∩not B) lls. These labels will update the labels in the probabilities area. cells. es tables. changed. The rest are locked. The calculator can be used with proportions or counts.

"Event

cy Tables for Probabilities using Counts Event A A Not A Totals 50 7 57 17 26 43 67 33 100 bilities Calculations ple Probabilities Event B P(B) = 0.5700 P(Not B) = 0.4300 Event A P(A) = 0.6700 P(Not A) = 0.3300 P(B and A) = 0.5000 P(B and Not A) = 0.0700 P(Not B and A) = 0.1700 P(Not B and Not A) = 0.2600 P(B or A) = 0.7400 P(B or Not A) = 0.8300 P(Not B or A) = 0.9300 P(Not B or Not A) = 0.5000 ties ("A GIVEN B" or "B GIVEN A") t A GIVEN Event B" P(B | A) = 0.7463 P(Not B | A) = 0.2537 P(B | Not A) = 0.2121 P(Not B | Not A) = 0.7879 babilities ("A AND B") on Rule ("A OR B")

Multiplication Rule Solve for? Choose from dropdown P(A and B) P(A and B) see solution below P(A|B) enter value 0.3 P(B) enter value 0.5 Solution P(A and B) 0.15 Multiplication Rule (Independent Events) Solve for? Choose from dropdown P(A) P(A and B) enter value 0.15 P(A) see solution below P(B) enter value 0.5 Solution P(A) #DIV/0! To use t from th and the For the blue dro occuring box.

the calculators for the Multiplication Rule, simply choose he blue dropdown the value that you are trying to solve for en enter the two required values next to the green boxes. rule of complements calculator, simply choose from the opdown whether you want the probability for event g or not occuring and enter the required value in the green Multiplication Rule P(A ∩ B)=P(A|B)*P(B) Multiplication Rule (Independent Events) P(A ∩ B)=P(A)*P(B) Rule of Complements P(A)= 1-P( 𝑨 ̅ )

Greater than X Excel Formula Greater than or equal to X Excel Formula mean Given mean Given SD Given SD Given X Given X Given P(>X)= Err:502 =1-NORM.DIST(C28,C26,C27,1) P(>/X)= Err:502 =1-NORM.DIST(G28,G26,G27,1) Less than X Excel Formula Less than or equal to X Excel Formula mean 75 Given mean 75 Given SD 20 Given SD 20 Given X 45 Given X 45 Given P(<X)= 0.067 =NORM.DIST(C57,C55,C56,1) P(>X)= 0.067 =NORM.DIST(G57,G55,G56,1) Less than X1 Less than X2 mean 75 mean 75 SD 20 SD 20 X1 65 X2 85 P(<X1)= 0.309 P(<X2)= 0.691 P(X1-X2) 0.383 NORMAL DISTRIBUTION mean SD NORMAL DISTRIBUTION mean SD NORMAL DISTRIBUTION mean SD NORMAL DISTRIBUTION mean SD HYPERLINK Fast online Calculator for Probability given mean and SD for a Normal distribution

Solving for X using NORM.INV if you are given the left sided probability… What X such as P(<X)= p? Excel Formula P(<X)=p Given, left sided, no need to adjust mean Given SD Given Solve for X Err:502 =NORM.INV(E27,E28,E29) Solving for X using NORM.INV if you are given the right sided probability… What X such as P(>X)= p? Excel Formula P(>X)=p Given, right sided, need to calculate the left sided probability 1st P(<X)=1-p 1 =1-E55 mean Given SD Given Solve for X Err:502 =NORM.INV(E56,E57,E58) Using NORM.INV HYPERLINK Fast online Calculator for X given area, mean and SD for a Normal distribution X=? X=? p given is the left sided probability. No need to adjust p 1-p X=? X=? ***If p given is the right sided probability, need to calculate first the left sided probability*** p Proportion given is the LEFT sided probability. (Remember: Always enter left sided probability in Excel) Proportion given is the LEFT sided probability. (Remember: Always enter left sided probability in Excel) Proportion given is the RIGHT sided probability. (Remember: Always enter left sided probability in Excel) Proportion given is the RIGHT sided probability. (Remember: Always enter left sided probability in Excel)

Equation Value n 40 p 0.25 n*p 10 sqrt(n*p*(1-p) 2.73861278752583 sqrt(mean*(1-p) 2.73861278752583 # successes given p(success) above 10 "=BINOM.DIST(X,n,p,TRUE)" 0.58390407802879 "=1- BINOM.DIST(X,n,p,TRUE)" 0.41609592197121 "=BINOM.DIST(X,n,p,FALSE)" 0.144364346356257 "=BINOM.DIST(X-1,n,p,TRUE)" 0.439539731672533 "=1- BINOM.DIST(X-1,n,p,TRUE)" 0.560460268327467 Equation Value n 40 p 0.75 n*p 30 sqrt(n*p*(1-p) 2.73861278752583 sqrt(mean*(1-p) 2.73861278752583 # failures given p(failure) above 10 "=BINOM.DIST(X,n,p,TRUE)" 4.63088089773928E-11 "=1- BINOM.DIST(X,n,p,TRUE)" 0.999999999953691 "=BINOM.DIST(X,n,p,FALSE)" 4.14032901818804E-11 "=BINOM.DIST(X-1,n,p,TRUE)" 4.90551879551258E-12 "=1- BINOM.DIST(X-1,n,p,TRUE)" 0.999999999995094 BINOMIAL DISTRIBUTION CALCULATOR (Successes) BINOMIAL DISTRIBUTION CALCULATOR (Failures)

Excel Equation Given Given =E4*E5 =SQRT(E4*E5*(1-E5)) =SQRT(E7*(1-E5)) Given =BINOM.DIST(E11,E4,E5,1) =1-BINOM.DIST(E11,E4,E5,1) =BINOM.DIST(E11,E4,E5,0) =BINOM.DIST(E11-1,E4,E5,1) =1-BINOM.DIST(E11-1,E4,E5,1) Excel Equation Given Given =E21*E22 =SQRT(E21*E22*(1-E22)) =SQRT(E24*(1-E22)) Given =BINOM.DIST(E28,E21,E22,1) =1-BINOM.DIST(E28,E21,E22,1) =BINOM.DIST(E28,E21,E22,0) =BINOM.DIST(E28-1,E21,E22,1) =1-BINOM.DIST(E28-1,E21,E22,1) These cal distributio or E21:23 Remembe outcomes Also reme for all val When you Please rem •If you ar probabilit •If you ar probabilit This calcu make sure

lculators to the left were designed as a quick way to calculate the mea on as well as probabilities. The formulas are built in. To use, just enter 3) boxes only. er, you can only use these when you have a discrete variable X ("coun s such as sell or don't sell, defective or not defective, buy or don't buy ember that when you use the equation =BINOM.DIST (X,n,p,TRUE) , Ex lues from 0 to X inclusive of X. u use the equation =BINOM.DIST(X,n,p,FALSE) , Excel calculates the pro member to pay attention to which p you enter in the calculator. In the re estimating the probability of no more than 10 customers " buying " l ty that a customer buys which is 0.25. re estimating the probability of no more than 10 customers " not buyin ty that a customer does not buy which is 0.75. ulator provides you with all the probabilities (P(</X), P(>X), P(X), P(<X) e you choose the answer that applies to the problem you are asked to

HYPERLINK Fast online Calculator for Binomial distribu