A bag contains 5 gold marbles, 10 silver marbles, and 26 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $5, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss if you play this game?

Accepted Solution

Answer:You will most likely lose $1 from playing this gameStep-by-step explanation:So lets look at the info they gave us...Gold-$5 (We have 5)Silver-$2 (We have 10)Black-$0 (We have 26)Total Marbles: 41So now we can find the probability of us picking each color and we will use the color with the highest probability to make the logical assumption of what our profits or loss will be, let's go!So the chances of us picking gold will be 5/41 because there are only five in the entire batch of 41 marbles, so that seems pretty lowThe chances of us picking a silver marble is 10/41 which is pretty decent, we have about a 25% chance, we'll keep that one in mind.The chances of us picking a black marble is 26/41, which is over 50 percent! We are going to use this color because the probability of us choosing it is over TWICE the probability of the other colors combined! Now we need to refocus on what the question is asking, "What is the expected profit or loss if you play this game?" Well we now know that we are expected to pick a black marble, which is worth nothing according to the info they gave us. Thus, we can make a conclusion that since we earn nothing, and we pay $1 to play the game, we will lose $1.Hope I helped!!!! :)