A lottery game is played as follows: Players choose 5 numbers from 1 through 39. Five winning numbers from 1 through 39 are chosen at random. Players win if they correctly choose all five winning numbers.
a) if 50,000 people play the game and choose their numbers at random and independently, what is the probability that at least one player wins?
b) use Boole's Inequality to obtain an upper bound on the probability that you computed in part a
I started with the probability of winning 1/(39 choose 5) = 1/575757 = .00000174
in part a. I wanted to just multiply (1/575757) by 50,000 but the answer to that is ~.086 and we're given the right answer to check. which should be .083.
I figure I can calculate how many ways there are to not win and multiply that by 49,999 but I'm not sure how to approach it
for part b I can't start without part a.
Oct 16th 2013, 02:28 AM
You need to remember that choosing a number affects the number of possibilities for the next set of choices. The first possibility is 39, the second is 38 and so on.
Do you know how to deal with situations that have sampling without replacement (as opposed to with replacement)? This will affect your probability very slightly (since 39 is large) but it will still have enough of an effect.