At a carnival, there is a game where you can draw one of 100 balls from a bucket. The balls are numbered from 1 to 100 . If the number on the ball is even, you win $13. If the number on the ball is odd, you win nothing. If you play the game, what is the expected payoff?

Question

At a carnival, there is a game where you can draw one of 100 balls from a bucket. The balls are numbered from 1 to 100 . If the number on the ball is even, you win  $13. If the number on the ball is odd, you win nothing. If you play the game, what is the expected payoff?

Bytelearn · Accepted Answer

Calculate probability of even number: Determine the probability of drawing an even-numbered ball. Since there are 100 balls numbered from 1 to 100, there are 50 even numbers and 50 odd numbers. Probability of drawing an even number = Number of even numbers / Total number of balls Probability of drawing an even number = 50 / 100Calculate expected payoff for even number: Calculate the expected payoff for drawing an even-numbered ball. The expected payoff for an event is calculated by multiplying the probability of the event by the payoff for that event. Expected payoff for even number = Probability of drawing an even number * Payoff for even number Expected payoff for even number = (50 / 100) * $13Perform expected payoff calculation: Perform the calculation for the expected payoff for drawing an even-numbered ball. Expected payoff for even number = 0.5 * $13 Expected payoff for even number = $6.50Calculate probability of odd number: Determine the probability of drawing an odd-numbered ball. Since there are 50 odd numbers out of 100 balls, the probability is the same as for even numbers. Probability of drawing an odd number = Number of odd numbers / Total number of balls Probability of drawing an odd number = 50 / 100Calculate expected payoff for odd number: Calculate the expected payoff for drawing an odd-numbered ball. Since the payoff for drawing an odd-numbered ball is $0, the expected payoff is: Expected payoff for odd number = Probability of drawing an odd number * Payoff for odd number Expected payoff for odd number = (50 / 100) * $0 Expected payoff for odd number = 0.5 * $0 Expected payoff for odd number = $0Calculate total expected payoff: Calculate the total expected payoff for playing the game. The total expected payoff is the sum of the expected payoffs for each possible outcome. Total expected payoff = Expected payoff for even number + Expected payoff for odd number Total expected payoff = $6.50 + $0 Total expected payoff = $6.50

At a carnival, there is a game where you can draw one of $100$ balls from a bucket. The balls are numbered from $1$ to $100$ . If the number on the ball is even, you win $\$ 13$ . If the number on the ball is odd, you win nothing. If you play the game, what is the expected payoff?

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At a carnival, there is a game where you can draw one of $100$ balls from a bucket. The balls are numbered from $1$ to $100$ . If the number on the ball is even, you win $\$ 13$ . If the number on the ball is odd, you win nothing. If you play the game, what is the expected payoff?