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