IHG promotional event will leverage a lottery but to keep from being sued they will be using the formula below to present details on any potential favoritism.
Based on the probabilities, it is most likely that someone selected from the 45-55 age group is selected, and it is more likely that a female is than a male.
Female Probability:
P(F) = 5600/10000
5600/10000 = .560 chance female
35-55 Age Probability:
P(A) = P(35-45) + P(45-55)
P(A) = (2500/10000) + (3500/10000)
.25 + .35 = .60 chance female
Female and 35-45 Age Probability:
P(An F) = (P(35-45) + P(45-55)) × P(F)
(78 + .237) x486 = .153 chance female and 18-40
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Female or 45-55 Age Probability.
P(A U F) = P(35-45) + P(45-55) + P(F) – P(A U F)
P(A U F) = (2500/10000) + (3500/10000) + (5600/10000) – .315
P(A UP) =.45 + .35 + .560 – .315
1.36 – .315 = 1.045 chance females 35-55