Question

Suppose that in a lottery there are n tickets, and m(< n) tickets will win a prize among them. Also, suppose that there are n players, and they will choose one ticket at random successively from the available tickets.

Does the third player, the player to choose his or her ticket after two players have already chosen their tickets, have a disadvantage over the second player or the 1st player?

Answer 1

Note that the probability of winning a lottery in any year is 100/1000000 = 1/10000=0.0001 = p

n = number of years ( trials ) = 10

Let X = number of lottery win by one of the specified person.

So here we want to find P ( X >= 1 ) = 1 - p( X = 0) .......( 1 )

Let P( X = 0) = P( he is not win a lottery in 10 years) = (1 - p)^10 = 0.9999^10 = 0.999

Plug this value inb equation ( 1 ) , we get

P ( X >= 1 ) = 1 - p( X = 0) = 1 - 0.999 = 0.001