# Choose from set

• Feb 26th 2007, 09:28 PM
pig
Choose from set
This is driving me buggy.

You have a set of 50 fruit. 10 of these fruit are apples. What is the probability of getting an apple if you choose 8 fruit at random?

TIA
• Feb 27th 2007, 09:16 AM
ThePerfectHacker
Quote:

Originally Posted by pig
This is driving me buggy.

You have a set of 50 fruit. 10 of these fruit are apples. What is the probability of getting an apple if you choose 8 fruit at random?

TIA

What is the probability of NOT getting an apple.

Meaning,
No apple on first try.
No apple on second try.
No apple on third try.
....

Thus, the probability for each one respectively are,
(40)/(50)
(39)/(49)*
(38)/(48)
...
(33)/(43)

Thus,
(40*39*38*...*33)/(50*49*...*43)=(40P8)/(50P8)=.1432
This is the probability of not getting an apple.

Thus, the probability of getting an apple is,
1-.1432=.8568

*)Because you now have 1 less of each fruit after your chose the first one.
• Feb 27th 2007, 09:27 AM
Plato
If C(N,k) means combination of N things choosing k then the probability of getting no apples is [C(40,8)/C(50,8)]. Thus the probability of getting at least one apple is 1-[C(40,8)/C(50,8)].
• Feb 27th 2007, 09:43 AM
Soroban
Hello, pig!

Quote:

You have a set of 50 fruit. .10 of these fruit are apples.
What is the probability of getting an apple if you choose 8 fruit at random?

There are: .C(50,8) .= .(50!)/(8!42!) .= .536,878,650 possible samples.

I assume that "getting an apple" means getting at least one apple.

The opposite of "at least one apple" is "no apples".

To get no apples, we choose 8 of the other 40 fruit.
. . There are: .C(40,8) .= .(40!)/(8!32!) .= .76,904,685 ways

Hence, there are: .536,878,650 - 76,904,685 .= .459,973,965 ways to get some apples.

. . . . . . . . . . . . . . . . . . . . . . .459,973,965
Therefore: . P(some apples) .= .---------------
. . . . . . . . . . . . . . . . . . . . . . .536,878,650

. . I'll let you reduce/simplify the fraction . . .

• Feb 27th 2007, 09:51 AM
ThePerfectHacker
Quote:

Originally Posted by Soroban
Hello, pig!

That sounds so funny.
• Feb 27th 2007, 10:35 AM
Soroban
I felt the same way . . .

Quote:

Originally Posted by ThePerfectHacker
That sounds so funny.

Rule #1: .Never use "Hello, pig" as a pick-up line.

• Feb 27th 2007, 12:52 PM
topsquark
Quote:

Originally Posted by Soroban
I felt the same way . . .

Rule #1: .Never use "Hello, pig" as a pick-up line.

...Or when you get pulled over... :eek:

-Dan
• Feb 27th 2007, 02:53 PM
ThePerfectHacker
Quote:

Originally Posted by topsquark
...Or when you get pulled over... :eek:

-Dan

No. This is what not to say.

[GVIDEO]2486751475289802990[/GVIDEO]
• Feb 27th 2007, 02:55 PM
Jhevon
Quote:

Originally Posted by ThePerfectHacker
No. This is what not to say.

[gvideo]2486751475289802990[/gvideo]

Ha ha, nice
• Feb 27th 2007, 09:19 PM
pig
Thanks for the info guys. I will digest it.