Double Head

Two fair coins are flipped simultaneously. This is done repeatedly until at least one of the coins comes up heads, at which point the process stops. What is the probability that both coins came up heads on the last flip?
Source: NCTM Mathematics Teacher 2006

SOLUTION
To get a feel for the problem we conduct 120 trials using the random generator function of a TI-83 Plus. The results are recorded in the spreadsheet below


While some trials end quickly with one double flip, others took longer with several double flips. What is important is not how long the trials take but how they end. They end in 3 possible ways: HH, TH, or HT. The probability that both coins came up heads on the last flip equals 1/3.
The spreadsheet shows that in the 120 trials the event HH occurs 40 times. The experimental probability = 40/120=1/3 dovetails with the theoretical probability.

Answer: 1/3

Advertisements

About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s