Probability of certain numbers

Question

If you pull 5 numbers from 1-69, not repeating, what is the probability of the number 1 being drawn, if it had been drawn 3 times out of 325

Answer 1

Stephanie L.,

Who cares what you got in the past draws? Each drawing of 5 numbers is independent. So, solve the usual way: --> 1 - P(1 NOT being drawn) = (68/69)*(67/68)*(66/67)*(65/66)*(64/65) = 64/69. [Since you keep decreasing your available set to choose from, the denominator keeps decreasing.]

This question would be more interesting if it had read: the number 1 was drawn 3 times out of 325 times, when a set of 5 numbers was drawn randomly without replacement from a set of (1, 2, ... n) integers. What is the MOST LIKELY value for n? Then, you would have to treat the Poisson distributions for draws of "1", for each n.

-- Cheers, --Mr. d.