Suppose that \($1\) lottery tickets have the following probabilities: 1 in 5 to win a free ticket (worth \($1)\), 1 in 100 to win \($5,\) 1 in 100,000 to win \($1,000\), and 1 in 10 million to win \($1\) million. What is the expected value of a lottery ticket? Discuss the implications. (Note: Winners do not get back the \($1\) they spend on the ticket.)