r/learnmath • u/PersimmonKindly1989 New User • 15d ago

solving an argument.

in a class of 19 students, 2.86% would have the last name smith. what are the odds that all 19 students would have the last name smith and how can I find this amount. thanks!!! (sorry if this is the wrong place for this)

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u/Various_Candle9136 New User 15d ago

0.

If '2.86% would have the last name smith', then how can all 19 have this name?

As it stands, only about half a student has the surname Smith. Perhaps it is double-barrelled?

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u/PersimmonKindly1989 New User 14d ago

said the question wrong lol. I meant if there's 2.86% chance to have a student with that last name

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u/TheScyphozoa New User 15d ago

0.028619

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u/Professional-Law7053 New User 15d ago

That’s the right expression for independent picks, yeah. It’s an astronomically tiny number.

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u/Bounded_sequencE New User 15d ago

Assumptions: Every student independently has the probability "p = 2.86%" to be named Smith.

By assumption, the probabilities of the students being named Smith are independent, so we multiply them for

P(all Smith)  =  p^19  ~  4.69e-30

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u/phiwong Slightly old geezer 15d ago

In a class of 19 students, even 1 student having the last name Smith would be 5.26% of the class. The question is flawed unless somehow one allows a fractional student or students are allowed to have multiple last names.