Question

if 30 students are asked to pick a number between 1 and 60, what is the probability at least 2 will choose the same number?

Answer 1

I'm really rusty with probability ... here is my attempt :)

Total Number of possibilities for 30 students to pick any number from 1 to 60:

T=60^30

Number of possibilities for 30 students to pick a number from 1 to 60, so that all their numbers are unique:

U=60!/30!

And the probability we are looking for is:
P=1-U/T = 1 - (60!/30!)/(60^30)

Answer 2

AT LEAST TWO a set up for "all are different"

Answer 3

its might be easier to find the probability of "at most 1 student "

Answer 4

is fiddlearound not correct?

Answer 5

that mighta been worded wrong; but im thinking its complememnt

Answer 6

fiddlearound is right.

Answer 7

since its saying at least 2 can pick the same # im thinking it has to do "with replacement" ...

Answer 8

...could this pass for a binomial probability as well?

Answer 9

you compute the probabilty that they are all different, then subtract from 1. the probability they are all different is most succinctly written as
\[\frac{\frac{60!}{30!}}{60^{30}}\]

Answer 10

i think you can approximate this with poisson, so i guess it relates to binomial, but i forget how. good luck computing this number!

Answer 11

fixed number of trials,
two outcomes,
probability stays the same
and one other factor that determines it if i have it right in me head

Answer 12

n= 30, p=1/60, q = 59/60 perhaps?

Answer 13

but we don't have 2 outcomes for each trial - or maybe I'm missing something ...

Answer 14

my thought, as wrong as it might be, comes to .08891

Answer 15

well, if the outcome is to get the same number; then the other option is to not get the same number ... but thats onlyh if i see it right

Answer 16

you are making me think too hard. i just recognize this as birthday problem. you can also compute via
\[(1-\frac{1}{60})(1-\frac{2}{60})...(1-\frac{29}{60})\] i think

Answer 17

http://www.wolframalpha.com/input/?i=1+-+%2860%21%2F30%21%29%2F%2860^30%29

wolfram gets the number 0.999....

Answer 18

the answer in the back of the book says the probability is almost 1

Answer 19

yes it should be very very close to one. it is almost certain that two will pick same number

Answer 20

Is that the answer they expect : "almost 1" ? :)

Answer 21

lol .... good, then I was wrong :)

Answer 22

yeah thats exactly the answer in the back of the book!

Answer 23

oh look at fillearound wolfram link. you see that it is .999858...

Answer 24

is the outside of the book fuzzy too?

Answer 25

hahahahah