Why can't you use the negative binomial here?

A box contains 10 balls, 3 of which are red. Balls are drawn randomly from the
box one at a time, without replacement. What is the probability that the last ball
drawn from the box is red?

Why couldn't you use the negative binomial for this?

Reply 1

ubarolsi

3

because the probability of success is not fixed - the initial probability of drawing a red is 3/10, but as the balls are not replaces, this probability changes

Reply 2

DFranklin

18

Original post by vitc83

A box contains 10 balls, 3 of which are red. Balls are drawn randomly from the
box one at a time, without replacement. What is the probability that the last ball
drawn from the box is red?

Why couldn't you use the negative binomial for this?

FWIW, it's perfectly possible to get the answer by inspection - you don't need to know about binomials or any other distribution.

Reply 3

Kallisto

Entertainment Forum Helper

22

Original post by vitc83

A box contains 10 balls, 3 of which are red. Balls are drawn randomly from the
box one at a time, without replacement. What is the probability that the last ball
drawn from the box is red?

Why couldn't you use the negative binomial for this?

For a negative binomial, the propability has to be always the same, but because of the missing replacement, it changes. So the number of drawn red balls are dependent, that would not be the case, if it is negative binomial.

(edited 11 months ago)

Why can't you use the negative binomial here?

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