A random variable Y can only take values in {−5, 0, 5}. The expected value of Y is 0 and its variance is 24. Find the probability distribution of Y .

Question

$Pr(-5)*(-5 - 0)^2 + Pr(O)*(0 - 0)^2 + Pr(5)*(5 - 0)^2 = 24$

$25*Pr(-5) + 0 + 25*Pr(5) = 24$

$25(Pr(-5) + Pr(5)) = 24$

$Pr(-5) + Pr(5) = 24/25$

$(-5 * Pr(-5)) + (0 * Pr(0)) + (5 * Pr(5)) = 0$

$(-5 * Pr(-5)) + (5 * Pr(5)) = 0$

$5(-Pr(-5) + Pr(5)) = 0$

$-Pr(-5) + Pr(5) = 0$

$Pr(-5) = Pr(5)$

Since they are equal to one another, can I say that: $Pr(-5) = Pr(5) = 12/25 ?$