Run through an array

Clojure, 41 37 bytes

(fn[a k](map #(+(*(rand-int 2)k)%)a))

Knocked off a couple of bytes by multiplying by 0 or 1 and dropping the "if". Credit to most all of the other submitters!

Jelly, 9 8 7 bytes

From 8 to 7 thanks to @FryAmTheEggman.

+2X’¤¡€

Try it online!

Explanation

+2X’¤¡€
      €   Map over each argument...
 2X           Choose a random number from {1,2}
   ’          Minus 1
    ¤                (grammar stuff)
     ¡        Repeat that number of times...
+                 Add the second input (to the argument being mapped over).

Pyth, 7

m+*O2vz

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Uses a random choice instead of floating point comparison, but should be indistinguishable.

Expansion:

m+*O2vz     ## implicitly, a d and Q are added to the end of the program
m+*O2vzdQ   ## Q = eval(input()), z= input()
m           ## map over each element d of Q
 +     d    ## add to d
  *O2vz     ## the product of eval(z) and a random number chosen from [0, 1]

Using floating point:

m+*<.5O0vz

Try it here