Captial Allocation

You manage an investment portfolio. Your investors have demanded a 95 percent probability that your investment strategy will grow the $17 million fund to $100 million. You have identified 11 companies, each of which has an 85 percent probability that each $1 invested will grow to $10, and a 15 percent probability that the investment will become worthless. Any funds not invested retain their original value.

Can you devise a strategy that meets your investors' requirement? Send your solution to ar@casact.org.

Highest Probability?

Tom Struppeck had suggested a puzzlement using a standard 52-card deck of cards. You flip cards until an ace appears. What is the probability that the next card is the ace of spades? (Deuce of clubs?).

Alan Jones's solution exhibited a puzzle solver's approach. His solution reads, in full, "Probability is 1/52 for both parts of the problem. Start with four cards, calculate; go to five cards, etc." Slightly more rigorously, consider shuffling the 51 cards other than the target card (ace of spades or deuce of clubs). There are 52 equally likely spots for the target card, exactly one of which is immediately following the first ace among the 51.

The following individuals sent solutions.

David Atkinson Taylor Barker Edward Baum Roger Bovard Geoff Bridges Frank Chang Jon Evans Shiwen Jiang Charles McClenahan Chris McKenna

Christopher Mosbo Misha Novakovic David Oakden Anthony Salido Steven Sousa Jean-François Tremblay David Uhland Russ Wenitsky Dave Westerberg Zhonghua Zhang