The Hope club had a fundraising raffle where they sold 3865 tickets for \( \$ 3 \) each. There was one first place prize worth \( \$ 955 \) and 4 second place prizes each worth \( \$ 10 \). The expected value can be computed by: \( E V=\frac{955+(10)(4)+(-3)(3865-1-4)}{3865} \) Find this expected value rounded to two decimal places (the nearest cent).

To calculate the expected value (EV), we first need to understand the components. The total prizes amount to \( \$ 955 + (4 \times \$ 10) = \$ 955 + \$ 40 = \$ 995 \). Now, let's address the losses. The total number of tickets sold is 3865, and each ticket costs \( \$ 3 \), so the total revenue from tickets sold is \( 3 \times 3865 = \$ 11,595 \). The expected value formula provided can be calculated as follows: \[ EV = \frac{995 + (-3)(3865 - 1 - 4)}{3865} \] This simplifies to: \[ EV = \frac{995 - 3(3860)}{3865} \] \[ = \frac{995 - 11580}{3865} = \frac{-10585}{3865} \approx -2.74 \] Rounded to two decimal places, the expected value is approximately \( -2.74 \). This negative value suggests that on average, participants lose \( \$ 2.74 \) for every ticket purchased.