SOA Conditional probability question I can't get this correct. Could you please provide a hint to aproach this problem? How do i get the probability of that loss? 
"A state is starting a lottery game. To enter this lottery, a player uses a
machine that randomly selects six distinct numbers from among the first 30
positive integers. The lottery randomly selects six distinct numbers from the
same 30 positive integers. A winning entry must match the same set of six
numbers that the lottery selected. The entry fee is 1, each winning entry
receives a prize amount of 500,000, and all other entries receive no prize.
Calculate the probability that the state will lose money, given that 800,000
entries are purchased."
 A: I guess you are to assume that tickets are purchased at random
and the numbers for a winning ticket are chosen at random; also,
to ignore the cost of running the lottery. Finally, the question
focuses on a single run of the lottery in which 800,000 tickets
are sold.
The probability any one ticket will win is $p = 1/{30 \choose 6}.$
If $n = 800,000$ tickets are sold then the the number of
winners is $X \sim \mathsf{Binom}(n, p).$ With a payout of
\$500,000 for each winning ticket, the state will lose money
whenever there are two or more payouts.
The probability the state will lose money on any one run of the lottery
with 800,000 tickets sold is $P(X \ge 2).$ A Poisson approximation seems
reasonable. The exact binomial probability from R is as follows:
p = 1/choose(30,6);  p
[1] 1.68414e-06
1 - pbinom(1, 800000,p)
[1] 0.3898443            # P(X > 1)               

Notes: (1) In the long run, the state would come out ahead. (2) The most common specific outcome is exactly one winner. (3) If there are two winners, most lotteries make them split the winning amount (4) A more typical scheme would be to keep the payouts at \$20,000 or \$25,000 until
there had been several runs of the lottery with no winners.
