STAT 100 Lecture Notes - Lecture 4: Life Insurance
15 Jun 2018
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1. (17.18)
(a) A persoal proailit epresses soeoe’s persoal judgeet aout ho likel a
outcome is. Bridget thinks her own chances of being divorced after age 64 are about
5%. This is the situation where the outcome of interest comes from a one-time
event, not from repeatable trials. If the probability were not personal, it would be
the same as the probability of being divorced for the randomly selected women over
64: 0.11, rather than 0.05.
(b) Bridget might think that her boyfriend/husband and she love each other very deeply
ad trul, so she does’t epet that she ill get diored. Or she ight know that
she is not likely to get married and therefore not likely to get divorced. Or she may
have a religious belief which opposes divorce so that she believes she is less likely to
be divorced.
(c) As a government official, I need to know the effect of the Social Security System on
retirement-aged divorced women, so I care only about the probability 0.11(sample
proportion) and the total number of retirement-aged women(population), and then
I can know how many retirement-aged divorced women there are. Besides, different
people have different personal probability of being divorced when they are over 64,
which is just their personal expectation or judgement about how likely an outcome
is. Therefore, personal probability cannot be referred reliably.
2. (17.22)
(a) The chance of getting any 4-digit number is 1/10000, because there are 4 positions,
each position you can choose any one digit from 0-9 to fill in, so there are
10*10*10*10=10000 total possible outcomes, and each one group 4-digit number
only exist one time, never repeating. Therefore, no matter which number you pick,
the probability to match the winning number is exactly same, 1/10000. Therefore,
either 2873 or 9999, these two outcomes have exactly the same probability.
(b) I think most people favor 2873 more, because, in their opinion, getting 4 same
number is a quite rare situation, most people think 9999 is less likely to be randomly
chosen as winning number. Even though 2873 is not a specific set of 4-digit number
but a more general number than 9999, in which all 4 digit are different. Most
numbers have all 4 different numbers: 10*9*8*7=5040. Therefore, there are 5040
groups having all 4 different numbers out of total possible outcome for 4-digit
numbers 10000. And if you want to get all 4 same number sequence, the probability
is only 10 out of 10000.
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3. (18.10)
(a) P (forested) = 0.45
P (not forested) = 1 – P (forested) = 1 - 0.45 = 0.55
Therefore, the probability that the acre chosen is not forested is 0.55.
(b) P (forest) = 0.45 ; P (pasture) = 0.03
P (forest or pasture) = P (forest) + P (pasture) = 0.45 + 0.03 = 0.48
Therefore, the probability that it is either forest or pasture is 0.48.
(c) P (neither forest nor pasture) = 1 – P (forest or pasture) = 1 – 0.48 = 0.52
Therefore, the probability that a randomly chosen acre in Canada is something other
than forest or pasture is 0.52.
4. (18.14)
Probability model
The number of spots
1
2
3
4
Probability
1/4
1/4
1/4
1/4
Because the tetrahedron is a pyramid with four faces which are triangles with all sides
equal in length, the probability to get each spots on the down-face should be exactly
same. Besides, the probability model above obeys the following rules: (1) the probability
to get each spot is a number between 0 and 1, which is 1/4; (2) Those four possible
outcomes together have probability 1, in this case, ¼ + ¼ + ¼ + ¼ = 1; (3) The probability
that a eet does’t our is 1 ius the proailit that the eet does our; 4 to
events have no outcomes in common, the probability that one or the other occurs is the
sum of their individual probabilities. Therefore, I think my model is at least close to
correct.
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STAT 100 Full Course Notes
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Document Summary
(17. 18) (a) a perso(cid:374)al pro(cid:271)a(cid:271)ilit(cid:455) e(cid:454)presses so(cid:373)eo(cid:374)e"s perso(cid:374)al judge(cid:373)e(cid:374)t a(cid:271)out ho(cid:449) likel(cid:455) a(cid:374) outcome is. Bridget thinks her own chances of being divorced after age 64 are about. This is the situation where the outcome of interest comes from a one-time event, not from repeatable trials. If the probability were not personal, it would be the same as the probability of being divorced for the randomly selected women over. 64: 0. 11, rather than 0. 05. (b) bridget might think that her boyfriend/husband and she love each other very deeply a(cid:374)d trul(cid:455), so she does(cid:374)"t e(cid:454)pe(cid:272)t that she (cid:449)ill get di(cid:448)or(cid:272)ed. Or she (cid:373)ight know that she is not likely to get married and therefore not likely to get divorced. I can know how many retirement-aged divorced women there are. Besides, different people have different personal probability of being divorced when they are over 64, which is just their personal expectation or judgement about how likely an outcome is.
