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

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- Feb 26th 2007, 09:28 PMpigChoose 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 AMThePerfectHacker
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 AMPlato
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 AMSoroban
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?

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 AMThePerfectHacker
- Feb 27th 2007, 10:35 AMSoroban
- Feb 27th 2007, 12:52 PMtopsquark
- Feb 27th 2007, 02:53 PMThePerfectHacker
- Feb 27th 2007, 02:55 PMJhevon
- Feb 27th 2007, 09:19 PMpig
Thanks for the info guys. I will digest it.