Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 843 — #851
19.5. Linearity of Expectation 843
Class Problems
Problem 19.21.
A classroom has sixteen desks in a 4 4 arrangement as shown below.
If there is a girl in front, behind, to the left, or to the right of a boy, then the two
flirt. One student may be in multiple flirting couples; for example, a student in a
corner of the classroom can flirt with up to two others, while a student in the center
can flirt with as many as four others. Suppose that desks are occupied mutually independently
by boys and girls with equal probability. What is the expected number
of flirting couples? Hint: Linearity.
Problem 19.22.
Here are seven propositions:
Note that:
x 1 OR x 3 OR x 7
x 5 OR x 6 OR x 7
x 2 OR x 4 OR x 6
x 4 OR x 5 OR x 7
x 3 OR x 5 OR x 8
x 9 OR x 8 OR x 2
x 3 OR x 9 OR x 4
1. Each proposition is the disjunction (OR) of three terms of the form x i or the
form x i .