Edit Problem

Year

Paper

Question Number

Course

Section

Worksheet Citation (for copying)

Click the copy button or select the text to copy this citation for use in worksheets.

Problem Text

Rosalind wants to join the Stepney Chess Club. In order to 
be accepted, she must play a challenge match consisting of several
games against 
Pardeep (the Club champion)
and Quentin (the Club secretary), in which she must win at least one
game against each of Pardeep and Quentin.
From past experience, she knows that
the probability of her winning a single game against 
Pardeep is $p$ and the probability of her 
winning a single game against Quentin is $q$,
where $0 < p < q < 1$.
\begin{questionparts}
\item
The challenge match consists of three games.
Before the match begins, Rosalind must choose either to 
play Pardeep twice and Quentin once or to play Quentin twice and
Pardeep once.
Show that she should choose  to play Pardeep twice. 
\item
In order to ease the entry requirements,
it is decided instead that the  challenge match will consist of 
four games. 
Now, before the match begins,
Rosalind must choose  whether to play Pardeep three times and 
Quentin once 
(strategy 1), or
to play Pardeep twice and Quentin twice (strategy 2) 
or to play  Pardeep once and Quentin three times (strategy~3).
Show that, if $q-p > \frac 12$, Rosalind should choose strategy 1.
If $q-p<\frac12$, give examples of values of $p$ and $q$ to show
that strategy 2 can be better or worse than strategy 1.
\end{questionparts}

Solution (Optional)

Preview

Problem

Solution

Cancel

Current Ratings

Difficulty Rating: 1600.0

Difficulty Comparisons: 0

Banger Rating: 1502.2

Banger Comparisons: 2