Calculating Probability: Selecting Balls from a Box

[chrisyuen]

Homework Statement

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.

(Answers:
(a) 8
(b) _kC₈ / ₂₀C₈
(c) 0.0538)

Homework Equations

Probability Formulae

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!

 

[yyat]

Hi chrisyuen,

You need to compute the conditional probability

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

 

[chrisyuen]

I got it!

Thank you very much!