Question

Probability question

Coach has one tennis scholarship left...

Answer 1

Do you know what the best strategy is?

Answer 2

don't pick the first boy. then pick the next boy that is taller than the first.

Answer 3

does 'one at a time' mean they exist the house at the same time ? kind of confused.

Answer 4

no. it means that they come out one after another

Answer 5

I see. So you assume that the best strategy is to choose not first one but second one without having look at the rest ?

Answer 6

no. Don't pick the first guy...then pick the first kid that comes out (after the first) that is taller then the original guy

Answer 7

the next tallest might not be the second boy

Answer 8

But the first one can be the tallest one ?

Answer 9

correct...then you end up picking the last one out of the house

Answer 10

can he choose second one after seeing the 3rd and 4th one ?

Answer 11

no

Answer 12

he only has the option to choose a boy right when they come out of the house

Answer 13

this is related to the Secretary Problem

https://en.wikipedia.org/wiki/Secretary_problem

Answer 14

they even give the probability

\[\Large\frac{r-1}{n} \sum_{i=r}^{n} \frac{1}{i-1}\]

in this case \(r=2\) and \(n=4\)

Answer 15

So always to avoid the first choose.

Answer 16

unless you have only one or two total choices

Answer 17

yeah, that's for sure.

Answer 18

here r equals 2 ?

Answer 19

yes...it is 2

r-1 is the number of boys you pass

so r-1=1

r=1+1=2

Answer 20

that makes sense.

Answer 21

\(\large \color{black}{\begin{align}
& \dfrac{0+1+\frac12+\frac13}{4} \hspace{.33em}\\~\\
\end{align}}\)