Question

A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 9 spots labeled $1, 18 spots labeled $2, and 1 spots labeled $10, how much should a player expect to win on average? Round to the nearest cent. Your Answer: Question 5 options: Answer

Answer 1

Answer:

$ 1.96

Step-by-step explanation:

Number of spots with outcome of $1 = 9

Number of spots with outcome of $2 = 18

Number of spots with outcome of $10 = 1

Total number of spots = 28

Probability that ball will land on $1 = $\frac{9}{28}$

Probability that ball will land on $2 = $\frac{18}{28}$

Probability that ball will land on $10 = $\frac{1}{28}$

The amount that player should expect to win on average in equal to expected value of the game. Expected value is calculated as the summation of product of probabilities with their respective outcomes.

i.e. for this case:

Expected Value will be:

$(1 \times \frac{9}{28})+(2 \times \frac{18}{28})+(10 \times \frac{1}{28})\\\\ =1.96$

This means, on average the player should expect to win $ 1.96