Problem Solving

{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}

A number is to be selected at random for the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)( 2x-5) = 0

Ans. 1/6

the solutions are X=5, -10 and 2.5

x=5 is not in our set, that means the probability is 2/12 = 1/6 ?

I hope I copied the equation correct and there is x-5

Please correct.

{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}

A number is to be selected at random for the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)( 2x-5) = 0

Important note : If any of the above three terms becomes zero then automatically the product becomes zero.
Hence if x = -10 the middle term would become zero.
If x = 2.5 then the last term would become zero.
Hence the probability = 2/12 = 1/6