Answer to Puzzle #10
Well, it took us a long time to come back to this one. We were hoping for some answers, but evidently the problem seemed too complex. Here’s the problem for those of you who didn’t read it:
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?
Little Johnny needs $400,080.62 in order to buy all the gifts. The only way to get that much money would be to buy a lotter ticket (option 1). The chance he wins the lottery is 1 in 1 billion, and the chance option 1 is picked is 1/4. Therefore the chance he would win is 1 in 4 billion or 0.000000025%. Note this problem is really easy, just looks tricky because of options 2,3,4.