Question

At the Royal Dragon Chinese restaurant, a slip in the fortune cookies indicates a dollar amount that will be subtracted from your total bill. A bag of 10 fortune cookies is given to you from which you will select one. If six fortune cookies contain '$1 off," three contain '$2 off," and one contains "$7 off," determine the expectation of a selection.

Answer 1

To find the expectation of a selection from the fortune cookies at the Royal Dragon Chinese restaurant, we can calculate the expected value of each dollar amount and sum them up. The expectation is $1.90.

Step-by-step explanation:

To find the expectation of a selection from the fortune cookies at the Royal Dragon Chinese restaurant, we can multiply the dollar amount on each cookie by its probability of being selected, and then sum them up. Let's calculate the expectation:

1. For the fortune cookies with '$1 off': Probability = 6/10 = 0.6. Expected value = 0.6 * $1 = $0.6.
2. For the fortune cookies with '$2 off': Probability = 3/10 = 0.3. Expected value = 0.3 * $2 = $0.6.
3. For the fortune cookie with '$7 off': Probability = 1/10 = 0.1. Expected value = 0.1 * $7 = $0.70.

Now, add up the expected values: $0.6 + $0.6 + $0.70 = $1.90.

Therefore, the expectation of a selection from the fortune cookies at the Royal Dragon Chinese restaurant is $1.90.