What are the chances of winning a lottery with a group of 52 people?

[moonman239]

Let's say 52 people enter a lottery. There are 252 tickets, and each one has a probability of (1/252) of having a winning number (in other words, 1 of them is the grand-prize ticket, 1 has a prize less valuable than the grand prize, and another one has a prize less valuable than that.). Everyone buys 5 tickets each except the more affluent two, who buy 6 each.

What are the odds that:

1) one of the more affluent people will win the grand prize
2) that person will not win the grand prize, but will win some prize
3) one of the less affluent people (a given person) will win the grand prize
?

As I think about it, the answer may be obvious:

1) P(winning the prize) = 6/252

2) P(winning either the 2nd or 3rd prize) = P(winning the 2nd prize) + P(winning the 3rd prize) = 4/252

3) P(less affluent person will win the grand prize) = 1/252.

 

[chiro]

Hey moonman239.

Hint: Remember for the first question there are two affluent people so you are considering P(1st affluent wins grand prize OR 2nd affluent wins grand prize).

For the second question you have two types of people (affluent and non-affluent) and so you get a conditional distribution on both of these attributes.

 

[haruspex]

Let's say 52 people enter a lottery. There are 252 tickets, ... Everyone buys 5 tickets each except the more affluent two, who buy 6 each.

(52-2)*5 + 2*6 = 262
Should it be 50 people?

What are the odds that:

1) one of the more affluent people will win the grand prize
2) that person will not win the grand prize, but will win some prize

Umm.. what person? That affluent person that won the grand prize? Doesn't seem to be any chance that same person will not win the grand prize!

3) P(less affluent person will win the grand prize) = 1/252.

How many tickets does a less affluent person buy?