On three rolls of a single​ die, you will lose ​$19 if a 3 turns up at least​ once, and you will win ​$5 otherwise. What is the expected value of the​ game?Let X be the random variable for the amount won on a single play of this game.

Answer:-16 centsStep-by-step explanation:We are given that on  three rolls of a single​ die, you will lose ​$19 if a 3 turns up at least​ once, and you will win ​$5 otherwise.We are to find the expected value of the game.P (at least one 5 in three rolls) = 1 - P (no. of 3 in three) = [tex]1-(\frac{3}{6} )^2[/tex] = 0.875P (other results) = 1 - 0.875 = 0.125Random game value = -19, +5Probabilities: 0.875, 0.125Expected game value (X) = 0.875 × (-19) + 0.125 × (5) = -16 centsTherefore, every time you play the game, you can expect to lose 16 cents