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8
PROBABILITY
PRIMER
WITH
DICE
12
8
Probability
Primer
with
Dice
You
are
given
two
fair
dice.
1.
Make
a
plot
of
the
possible
outcomes
of
one
toss
of
one
die,
versus
the
likelihood
(probability)
of
that
outcome.
Clearly
there
are
six
possible
outcomes,
with
equal
likelihoods
of
occurring.
We
call
this
graph
a
probability
mass
function,
or
pmf.
probability
1/6
12
345
6
2
7
1
experiment outcome: x
1
experiment outcome: x
1
+ x
2
2.
Make
a
similar
plot
for
a
throw
of
both
dice,
where
the
outcome
is
the
sum
of
the
values,
i.e.,
the
outcome
of
a
toss
giving
[3,4]
is
seven.
Your
pmf
should
account
for
the
fact
that
there
are
more
ways
to
roll
a
three
([1+2],[2+1])
than
to
roll
a
([1,1]).
Solution:
As
shown
in
the
ﬁgure,
the
pmf
for
the
twothrow
case
has
a
nice
linear
structure.
The
height
of
each
spike
follows
the
possible
number
of
ways
the
additions
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.
 Spring '05
 GeorgeKocur

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