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© 2014 Pacific Crest
121
Step
Explanation
Watch it Work!
6. Calculate the
likelihood
Calculate the ratio of the number of
outcomes in event to the number
of outcomes in the sample space
(probability)
210 / 1024 = 105/512 = 20.5%
7. Validate
The total number of outcomes of all
other events added to the number of
outcomes in the defined event should
equal the number of outcomes in the
sample space.
C(10,0) + C(10,1) + C(10,2) +
C(10,3) + c(10,5) + C(10,6) +
C(10,7) + C(10,8) + C(10,9) +
C(10,10) = 1 + 10 + 45 + 120 +
252 + 210 + 120 + 45 + 10 +1 =
814 thus 1024 - 814 = 210
O
ops
! A
voiding
C
ommon
E
rrors
●
Belief that current series of actual events occurring influences future likelihood
Example
: The previous generation of cousins was comprised of 15 males and 3 females. The
current generation consists of 12 females and 3 males. The prediction is therefore that
the next child is more likely to be female.
Why?
Unless this new information causes the likelihood for this sample space to be
recalculated, the past events don’t impact the likelihood of future events. For example,
what is called “a 100 year storm” could happen twice in 20 years and this wouldn’t
impact future likelihood, unless experts have concluded that major climate patterns
have changed. In that case, they will change the likelihoods of the sample space.
●
Not precisely defining an event you are enumerating
Example
: A straight flush in poker is five consecutive cards of the same suit. Therefore, the
number of possible straight flushes is 8 (calculated as 13 – 5).
Why?
We must absolutely define the event. In the case of a straight flush, it matters that
there are four different suits, not just one. Additionally, of the 13 cards, in each suit,
the ace can begin a flush (ace, 2, 3, 4, 5: “low straight flush”) or end a flush (10, jack,
queen, king, ace: “high straight flush” or “royal flush”). Thus there are 10 possible
straight flushes in each suit for a total of 40 possible straight flushes across all suits.
●
Correctly differentiating the likelihood of an event
Example
:
Autism is a rare occurrence while being hit by lightening is unlikely and getting either a
full house, flush, or straight on a single draw is very rare.
Why?
Look at the actual measure of likelihood and the likelihood of each event:
Being struck by lightning: 0.0001% chance
Drawing a full house, flush or straight: 0.2% chance
Occurrence of an autism spectrum disorder in the general population: 1.5%
Ranking them:
very rare
rare
unlikely
less than 0.1%
0.1% to 1% 1% to 5%
being struck by lightning
poker hands
autism
0.0001%
0.2%
1.5%
3.1 Likelihood