# Homework Help: Probability 2

1. Mar 22, 2009

### chrisyuen

1. The problem statement, all variables and given/known data

Twenty balls labelled 1 through 20 are put in a box. Eight balls are randomly selected from the box without replacement. Let x denote the largest number selected.
(a) Denote by m the smallest possible value of x. Write down the value of m.
(b) Let k be any integer such that m<=k<=20. Express P(x<=k) in terms of k.
(c) It is known that x>15. Find the probability that x is 16.

(a) 8
(b) kC8 / 20C8
(c) 0.0538)

2. Relevant equations

Probability Formulae

3. The attempt at a solution

I know how to solve parts (a) and (b) but not part (c).

I tried part (c) as follows:
P(x=16)
= P(x<=16) - P(x<=15)
= (16C8 - 15C8) / 20C8
= 0.0511

However, the answer is not correct.

Can anyone tell me how to solve it?

Thank you very much!

2. Mar 22, 2009

### yyat

Hi chrisyuen,

You need to compute the conditional probability

P(x=16|x>15) = P(x=16)/P(x>15)

3. Mar 23, 2009

### chrisyuen

I got it!

Thank you very much!