Probability

February 12th, 2017

J/S: The Beatles are due on stage in one hour.

Ringo is in the dressing room at the stadium.  It takes him 1/2 hour to choose red things to wear.  It takes him 3 times as long to choose blue things as red.

George is hungry, and there is a 90% chance that he will see a restaurant, a 70% chance that he will go in, and an 80% chance that someone will see him, and a 25% chance that they will know everything about him, and a 60% chance that they will want to study his teeth to see if he really is a vampire for more than an hour.

John is on a date, and dates take 40 minutes per girl, and 3/5 of his dates are with one girl.  40% are with 2 or more girls.

Paul is walking to the stadium, disguised.  Along the way, there is a 30% chance that he will notice George in a restaurant and want to join him, and there is a 15% chance that the George fangirls examining George’s vampire teeth are actually Paul fangirls and they will turn around and kidnap him, and they will have replaced the restaurant employees with robots, and they will have shut down the telephone, and they will have AK-47s, so George won’t be able to do anything, and there is a 30% chance that the AK-47s will jam, and George will succeed in rescuing Paul.  Back on the street, if none of that happened, there is a 50% chance that Paul will be recognized by fans and chased all the way to the stadium, and will get there early.  He will have nothing to do, so he’ll go to the dressing room and find Ringo there, and they will have a long argument about the colors Ringo should wear, and there is a 50% chance that it will take too long.

S: Here comes the math…  WARNING: This probably won’t make sense. It certainly doesn’t make sense to me.

J: R_{on time} = 50% (1-25%) = 37.5%

PG_OT = 92%, P_late = 88.85%

PG_L = 0.9 · 0.7 · 0.8 · 0.25 · 0.6

PR_OT = 1/2

PG_OT = 1 – PG_L – 1 – 0.0756 = 0.92435

PJ_OT = 60% (40% · 10% PG goes in) – 60% + 4% = 64%

P_LKN = 0.3 · [(G_L = 0.9 · 0.7 · 0.8 · 0.25 · 0.60) = 92%) · 0.15 · (1 – 30%)] = 0.3 · 0.92 · 0.15 · 0.7 = 0.02898

P_LDRA = 50% · 50% = 25% = 0.25

P_L = P_LKN + P_LDRA = 0.02898 + 0.25 = 0.27898

P_OT = (1 – P_L) = 0.72102

J/S: Wilfrid Brambell is going out to lunch.  There is a 10% chance that he will eat at the restaurant where John is and make sure that he won’t be late to the show.  There is a 10% chance that he will eat at Paul and George’s restaurant and decide to be a king mixer there and order 100-year-old scotch that is very expensive, and there is a 50% chance that he won’t get away with it and Paul and George have to rescue him.  There is an 80% chance that he’ll eat somewhere else.

J: Math adjustment: P_OT = 0.72102 – P_late-grandad = 0.71157

10% Grandpa goes in

90% · 70% George goes in

50% rescue needed, George is late

PG_{late-grandad-rescue} = 10% · 90% · 70% · 50% = 0.0315

10% Grandpa goes in

30% Paul not as George goes in · 90% · 70%

50% rescue failed, Paul is late

Paul late Grandad rescue = 0.00945

J/S: Q1: What is the probability that at least one Beatle is on stage on time?

A1: 99.264012375%

Q2: What is the probability that ALL the Fab Four are on time?

A2: 15%

Q3: If it costs £100,000 if a concert must be canceled, and Brian wants to insure their concerts, how much should the insurance company charge per concert at minimum to break even?

A3: £85,000