Home Back to the Challenge Try These Think About This... Did You Know? Resources Try Another Challenge
Figure This!

The probability that your team wins is 9/16, or about 56% of the time.

Complete Solution:
There are many ways to answer the question:

Make a rectangular diagram with four rows of the same size. Shade three of the four rows to represent making the first shot.


Make four columns of the same size and shade three of them to represent making the second shot.


There should now be 16 cells in the grid. The 9 cells that are shaded twice represent success on both shots which means your team wins without any overtime play. Since 9 of the 16 equally likely outcomes reresents wins, the probability of winning is 9/16.

Complete Solution (cont.)
A different strategy is to draw a tree diagram labeled with all outcomes and their probabilities for each shot. The probability of winning is found by multiplying the probabilities on the appropriate brances of the tree.

If your teammate makes the first shot 3/4 of the time, then 3/4 of those times that she makes the first shot, she will make the second shot; that is:

(3/4) × (3/4) = 9/16

In this case, the probability of winning without overtime is 9/16.

[Multiplying probabilities here is correct only if the two shots are independent events. Assume that they are.]

Home · Back to the Challenge · Try These · Think About This  ·  Did You Know? · Resources
Try Another Challenge · Challenge Index · Math Index · Printing the Challenges · En Español
Family Corner · Teacher Corner · About Figure This! · Purchase the CD
©2004 National Council of Teachers of Mathematics
Web site and CD-ROM design/production
© 1999-2004 KnowNet Construction, Inc.