The college student senate is sponsoring a spring break Caribbean cruise raffle. The proceeds are to be donated to the Samaritan Center for the Homeless. A local travel agency donated the cruise, valued at $$2000.$ The students sold $2646$ raffle tickets at $$5$ per ticket.

$($a$)$ Kevin bought twenty$-$seven tickets. What is the probability that Kevin will win the spring break cruise to the Caribbean? $($Round your answer to five decimal places.$)$

What is the probability that Kevin will not win the cruise? $($Round your answer to five decimal places.$)$

$($b$)$ Expected earnings can be found by multiplying the value of the cruise by the probability that Kevin will win. What are Kevin's expected earnings? $($Round your answer to two decimal places.$)$

$

Is this more or less than the amount Kevin paid for the twenty$-$seven tickets?

How much did Kevin effectively contribute to the Samaritan Center for the Homeless? $($Round your answer to two decimal places.$)$

$