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Omni-MATH / Among citizens of Cambridge there exist 8 different types of blood antigens. In…

Problem

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problem

Among citizens of Cambridge there exist 8 different types of blood antigens. In a crowded lecture hall are 256 students, each of whom has a blood type corresponding to a distinct subset of the antigens; the remaining of the antigens are foreign to them. Quito the Mosquito flies around the lecture hall, picks a subset of the students uniformly at random, and bites the chosen students in a random order. After biting a student, Quito stores a bit of any antigens that student had. A student bitten while Quito had kk blood antigen foreign to him/her will suffer for kk hours. What is the expected total suffering of all 256 students, in hours?
Plain-text mathematical notation (without MathML)
Among citizens of Cambridge there exist 8 different types of blood antigens. In a crowded lecture hall are 256 students, each of whom has a blood type corresponding to a distinct subset of the antigens; the remaining of the antigens are foreign to them. Quito the Mosquito flies around the lecture hall, picks a subset of the students uniformly at random, and bites the chosen students in a random order. After biting a student, Quito stores a bit of any antigens that student had. A student bitten while Quito had k blood antigen foreign to him/her will suffer for k hours. What is the expected total suffering of all 256 students, in hours?
Original LaTeX notation
Among citizens of Cambridge there exist 8 different types of blood antigens. In a crowded lecture hall are 256 students, each of whom has a blood type corresponding to a distinct subset of the antigens; the remaining of the antigens are foreign to them. Quito the Mosquito flies around the lecture hall, picks a subset of the students uniformly at random, and bites the chosen students in a random order. After biting a student, Quito stores a bit of any antigens that student had. A student bitten while Quito had $k$ blood antigen foreign to him/her will suffer for $k$ hours. What is the expected total suffering of all 256 students, in hours?

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Source and history

task_id
426fb364-0371-5a46-94d6-7fb191e3d911
task_key
test--426fb364-0371-5a46-94d6-7fb191e3d911
task_revision_id
1
config / split
/ test

Official source

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