January 20, 2003
Problem of the Month

The Jelly Bean Problem
by Marilyn vos Savant

Carrie has two tiny bags of jelly beans.

Each bag contains two red jelly beans and two yellow ones (four jelly beans per bag -- a total of eight in the two bags).

She loves yellow jelly beans.

If she reaches in the bags and takes out one jelly bean from each, what are the chances that she'll get at least one yellow jelly bean?

Solution to the Problem:

The chances are 3 out of 4 that she will get at least one yellow jelly bean.   And interestingly, the chances are also 3 out of 4 that she will get at least one red one.

Mathematically, the probability that Carrie will get at least one yellow jelly bean is equal to 1 minus the probability that she will get no yellow jelly beans.

The probability that she will not get a yellow jelly bean is .25 or 1/4 (you multiply 1/2 * 1/2).   This is the same as the probability of getting two red jelly beans.

Therefore,
P(at least 1 Yellow) = 1 - 1/4 = 3/4.

Correctly solved by:

1. Adam Carter	Fort Wayne, Indiana
2. Andrea Eberhard	Columbus, Ohio
3. James Alarie	University of Michigan -- Flint Flint, Michigan
4. Rick Jones	Kennett Square, Pennsylvania
5. Richard Johnson	La Jolla, California
6. Paula Jones	Columbus, Georgia
7. Tina Zahel	Winchester, Virginia
8. William Funk and William Funk, Jr.	San Antonio, Texas
9. Elizabeth Harp	Columbus, Georgia
10. Keith Mealy	Cincinnati, Ohio
11. John Funk	Ventura, California
12. Jeff Gaither	Winchester, Virginia
13. David & Judy Dixon	Bennettsville, South Carolina
14. Johan Bernström	Tullängen, Sweden
15. Matt Stillwagon	Winchester, Virginia

Send any comments or questions to: David Pleacher