Question

A bag contains five Gold marbles, seven silver marbles and 23 black marbles. The rules of the game are as follows: you randomly select one marble from the bag. If it is gold you win six dollars, if it is silver you win two dollars. It costs one dollar to play. What is your expected profit or loss if you play the game?

Answer 1

The expected profit of playing the game is $0.77 per game.

Step-by-step explanation:

To calculate the expected profit or loss, we need to find the probability of winning and losing.

The probability of selecting a gold marble is 5/35, the probability of selecting a silver marble is 7/35, and the probability of selecting a black marble is 23/35.

The expected profit is the sum of the products of the probabilities and the corresponding winnings/losses: (5/35) x $6 + (7/35) x $2 - (23/35) x $1. Simplifying, we get an expected profit of $0.77.

Therefore, if you play the game many times, on average, you can expect to make a profit of $0.77 per game.