Puzzle #10: Mother’s Day Malady
Happy Mother’s Day!
Little Johnny wanted to get his mother a gift for Mother’s Day. Unfortunately he only had 96 cents. Johnny decided that he had 4 possible solutions to his problem:
- Spend his money on his lottery ticket. In this scenario there is a 9/10 chance he will lose all his money, a 1/20 chance he will double his money, an 0.049999999 chance he multiply his money by 10, and a 1 in 1 billion chance he will multiply his money by 1 million.
- Invest his money in a fast yielding government bond, ensuring him 2% of interest. This is, of course, excepting the unlikely event that the U.S. government would be destroyed before Johnny could claim his yield, a 1 in 10 billion chance resulting in Johnny losing all of his money as well as some other problems . Note: You cannot get a deal like this in the real world. It was a special limited offer for children with epithet, “Little.”
- Borrow some money from the neighbor kid~$8 dollars to be exact. The neighbor kid only deals in whole dollar multiples of 8 and only has 10 dollars. There is, however, a 1/10 chance that Johnny will fail to pay off his debt a weak later and get beat up.
- Go scrounging around the local park for loose change. There is a 40% chance he will find a dollar’s worth, a 30% chance he will find between 20 and 80 cents, a 10% chance he will find $5 worth, a 19.8% chance he will find nothing, and a 0.2% chance he will find $50 dollars’ worth. Don’t ask how I know all this.
Johnny will pick which plan to carry out randomly, each plan having an equal chance. The gifts Johnny has in mind for his mother are a cheap yo-yo (97 cents), an issue of People magazine ($1.84), a bouquet of tulips ($7.84), a pair of nice sunglasses ($28.98), a tempurpedic pillow ($40.99), or a rustic hunting lodge in Wyoming ($400,000). All prices include tax. Johnny will buy the highest price gift he can afford. What is the probability that Little Johnny’s mom will receive each of these gifts?
