In the casino game chuck-a-luck, three fair six-sided dice are rolled, and their outcomes are independent. the player loses $1 if no fives are rolled. the player wins $1 for each five that is rolled. let x be a random variable denoting the amount of money won or lost by the player during one round of this game. the possible values of x are -1, 1, 2, or 3. (hint: consider the three events e1 that the first die shows a five, e2 that the second die shows a five, and e3 that the third die shows a five. notice these events are mutually independent.)

answer: add the !

step-by-step explanation: then we will answer

congruent segments

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)