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patient”, C
“to be an unaffected patient”, de-
scendants from a couple, both being carriers of an autosomal recessive disease Z
have the following associated probabilities: P
=
“to be a carrier patient” and U
=
(
)=
.
(
)=
.
+
.
=
.
A
0
25; P
C
0
25
0
25
0
5;
(
)=
.
P
25. Thus, the probability of having a descendant that will enjoy a good
quality of life is P
U
0
75. If we think for a while in this situation, and
from a purely mathematical viewpoint, the decision of having a child under normal
circumstances is no more and no less than a common accorded bet between two
adults for “producing” a healthy child with an associated perceived probability of
such an occurrence that can at least be described as “very high”. In this point, we
must remark the fact that the perceived probability from wealthy parents of having a
healthy child is usually just 100%. Needless to say, such a perception is never com-
pletely true, among other reasons, because a Gaussian distribution has asymptotic
tails.
To speak about bets implies to speak about games. In order to better express
the idea behind this section, we can modify the autosomal recessive transmission
example, transform it with other words, and enunciate the following game, where
we bet one Euro (i.e. through a random device or system, like extracting some
coloured balls from a bag) with the associated probabilities shown in table 20.1:
(
U
)+
P
(
C
)=
0
.
Table 20.1 The case of 1 Euro bet and associated probabilities (read text)
Event Probability value
Result
To win
0.25
We win 1 Euro.
To tie
0.50
Neither lose nor win.
To lose
0.25
We lose 1 Euro.
It seems a good, equitable game at first. Now, we can develop another trans-
formation for the same game, this time changing the bet value. Let us imagine we
bet 50
000 Euros from our own savings. The probabilities and derived results are
shown in table 20.2:
,
Table 20.2 The case of 50,000 Euros bet and associated probabilities (read text)
Event Probability value
Result
To win
0.25
We win 50,000 Euros.
To tie
0.50
Neither lose nor win.
To lose
0.25
We lose 50,000 Euros.
Now, our perception of probability has changed and the risk of losing our bet
seems to have dramatically grown. This is known as “subjective probability”, that
is, a probability derived from an individual's personal judgement about whether a
specific outcome is likely to occur. In broad terms, subjective probabilities contain
no formal calculations and only reflect the subject's opinions and past experiences.
 
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