NUMB3RS - All's Fair - Guess My Type or Lose

Algebra 2 / Pre-Calculus / Statistics

TI Activity PDF

Matching Pennies and Tree Diagrams

Consider a classic game of matching pennies. If both coins match (Heads-Heads or Tails-Tails), Player A wins. Otherwise, Player B wins.

Suppose Player B suspects that Player A has a bias and plays Heads 60%60\% (0.60.6) of the time, and Tails 40%40\% (0.40.4) of the time. Player B wants to strategically set their own probability of playing Heads, which we will define as the variable xx. Consequently, the probability of Player B playing Tails is 1−x1 - x.

What is the algebraic expression for the probability that both players show Heads, P(H,H)P(H, H)?

0.50

Matching Pennies Probability Tree

Player B wins if coins don't match (HT or TH).

P(B Wins)
0.500
=
Win Threshold
0.500

Calculation: 0.6(1−0.50)+0.4(0.50)=0.5000.6(1 - 0.50) + 0.4(0.50) = 0.500