Question

There are 20 players on the school's water polo team. 8 of them are freshmen. The coach needs 8 starters. Determine the probability that the 8 freshmen will be randomly selected to be starters.

A. 7/5,168
B. 1/125,970
C. 7/41,990
D. 1/5,168

Answer 1

@pgpilot326

Answer 2

wouldnt my answer be C?

Answer 3

you know how to do this... give it a shot and I'll check your answer.

oops, just a sec...

Answer 4

not C

Answer 5

it looks like A

Answer 6

nope, looks like you're guessing...

Answer 7

so think of it,
at the beginning
what is the probability to choose a freshman ?

Answer 8

1 right?

Answer 9

1/5,168

Answer 10

look, you have a team of 20 players and 8 of them are freshman
so the probability that the first one that you choose is a freshman is 8/20

Answer 11

understand so far ?

Answer 12

yes

Answer 13

now, when we took one,
we left with a team of 19 where 7 of them are fresh ..
so what is the probability for the second one to be fresh ?

Answer 14

12 right?

Answer 15

why 12 ? (the probability cant be larger than 1 !!)

Answer 16

okay im very confused atm, lol then obiously it must be 1 lol.

Answer 17

look , when we first had 20 people and 8 of them were fresh
the probability to choose fresh was
8/20

Answer 18

now, we have 19 people and 7 of them are fresh
so what is the probability to choose a fresh now ?

Answer 19

it can also be thought of using combinations...

there are 8 starters and 20 players.

since you are choosing without replacement and order doesn't matter you can you combinations.

the total number of different starting lineups are \[\left(\begin{matrix}20 \\ 8\end{matrix}\right)\] this is the denominator.

Since there are 8 freshman and 12 non-freshmen and you need 8 of the freshmen and none of the non-freshmen, there is only 1 way to get this outcome: by choosing all of the freshmen.

so the numerator would look like this: \[\left(\begin{matrix}8 \\ 8\end{matrix}\right)\left(\begin{matrix}12 \\ 0\end{matrix}\right)\] both of these combinations have a value of 1.

it's not crucial to use this method in this problem, but there are situations which are more complex in which it is very useful to use combinations. just saying...

Answer 20

1

Answer 21

BTW, let X=# of freshmen chosen. then X ~ Hypergeometric (n=20, k= 8, r = sample size)

and

\[P(X=x)=\frac{ \left(\begin{matrix}k \\ x\end{matrix}\right) \left(\begin{matrix}n-k \\ r-x\end{matrix}\right)}{ \left(\begin{matrix}n \\ r\end{matrix}\right) }\text{ } \forall x,\,\, 0 \le x \le k \le r\]

Answer 22

the answer is B.

Answer 23

compute \[\left(\begin{matrix}20 \\ 8\end{matrix}\right) = \frac{ 20! }{(8!)( 12!) }\]

Answer 24

show me please...

Answer 25

just want to make sure you're getting it.

Answer 26

20/96= 0.20833333333

Answer 27

sorry...

did you follow my example?