12 pts In a certain lottery you pick a threedigit number fro

(12 pts) In a certain lottery, you pick a three-digit number from 000 to 999, and a randomly chosen winning three-digit number is announced every evening at 6:00 pm. If you pick a number with three distinct digits, you win S580 if your number matches the winning number exactly, and you win $80 if the digits of your number match the digits of the winning number, but in a different order. What is the expected value of the amount of money you win?

Solution

In a certain lottery you pick a three digit number from 000 to 999 and a randomly chosen winning three digit number is announced every evening at 6:00 pm.

If you pick a number with three distinct digits you win $580 if your number matches the winning number exactly and

you win $80 if the digits of your number match the digits of the winning number but in a different order.

Let X be the random variable as net profit.

There are total 10 digits.

P(winning $580) = 1/10 * 1/10 * 1/10 = 0.001

P(winning $80) = 1/10 * 1/10 * 1/10 = 0.001

So here X can take the values $580 and %80 with probabilities 0.001 and 0.001 respectively.

Expected value of winning = 580 * 0.001 + 80 * 0.001 = 0.66

Here we have to calculate only expected winning.