The 3-person jury makes its decisions based on majority rule. Jurors \(A\) and \(B\) each have probability \(p\) of making the right decision, while Juror \(C\) has a probability of \(\frac{1}{2}\) of making the right decision. The cases where they make the right decision are as follows (where \(R\) represents a right decision, and \(W\) represents a wrong one):

Juror A | Juror B | Juror C |
---|---|---|

R | R | R |

R | R | W |

R | W | R |

W | R | R |

Summing the probabilities of these 4 individual cases gives:

\[\frac{p^2}{2} + \frac{p^2}{2} + \frac{p(1-p)}{2} + \frac{p(1-p)}{2} = p\]

Thus, the 1-person and 3-person juries both have the same probability of making the right decision.