Hi. Please see attached. Thankyou! Conditional Probability. On September 3rd, the Italian National Institute of Healthpublished the following table regarding the Covid-19 pandemic situation in Italy in theprevious month.PopulationNot VaccinatedOne-Dose VaccineComplete Vaccination12-3981656253447156582277440-5952631931734907114936060-7919269377762301086961280+3008921073174145898DiagnosedSars-Cov-2Not VaccinatedOne-Dose VaccineComplete Vaccination12-3969504122171109740-592870147661460160-7981391785102780+1593157440HospitalizedNot VaccinatedOne-Dose VaccineComplete Vaccination12-3916261059340-59223513021360-79156219560780+56550875IntensiveTherapyNot VaccinatedOne-Dose VaccineComplete Vaccination12-3962240-5924981960-79286156680+4440DeceasedNot VaccinatedOne-Dose VaccineComplete Vaccination12-39440-59566860-79164184080+15913139Source: Italian National Institute of Health, September 3, 2021 c. For the age group 40-59, what is the probability of ending up in IntensiveTherapy for each of the three categories (not-vaccinated, partially vaccinated,fully vaccinated)? [Example: what is the probability of ending up in IntensiveTherapy, conditional on being a 40-59 non-vaccinated?]

Answered: c. For the age group 40-59, what is the…

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Hi. Please see attached. Thankyou!

Conditional Probability. On September 3rd, the Italian National Institute of Health
published the following table regarding the Covid-19 pandemic situation in Italy in the
previous month.
Population
Not Vaccinated
One-Dose Vaccine
Complete Vaccination
12-39
8165625
3447156
5822774
40-59
5263193
1734907
1149360
60-79
1926937
776230
10869612
80+
300892
107317
4145898
Diagnosed
Sars-Cov-2
Not Vaccinated
One-Dose Vaccine
Complete Vaccination
12-39
69504
12217
11097
40-59
28701
4766
14601
60-79
8139
1785
1027
80+
1593
157
440
Hospitalized
Not Vaccinated
One-Dose Vaccine
Complete Vaccination
12-39
1626
105
93
40-59
2235
130
213
60-79
1562
195
607
80+
565
50
875
Intensive
Therapy
Not Vaccinated
One-Dose Vaccine
Complete Vaccination
12-39
62
2
40-59
249
8
19
60-79
286
15
66
80+
44
40
Deceased
Not Vaccinated
One-Dose Vaccine
Complete Vaccination
12-39
4
40-59
56
6
8
60-79
164
18
40
80+
159
13
139
Source: Italian National Institute of Health, September 3, 2021

c. For the age group 40-59, what is the probability of ending up in Intensive
Therapy for each of the three categories (not-vaccinated, partially vaccinated,
fully vaccinated)? [Example: what is the probability of ending up in Intensive
Therapy, conditional on being a 40-59 non-vaccinated?]

Expert Solution

Step 1

If the probability of getting selected for each outcome is equal then such outcomes can be termed as equally likely outcomes. For equally likely outcomes, the probability of favorable event can be given by dividing the number of favorable outcomes, with the total number of outcomes.
$P r o b a b i l i t y o f f a v o r a b l e e v e n t = \frac{N u m b e r o f f a v o r a b l e o u t c o m e s}{T o t a l n u m b e r o f o u t c o m e s}$

The conditional probability of happening of event A when event B already happened, can be expressed as, $P (A B)$ .

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c. For the age group 40-59, what is the probability of ending up in Intensive Therapy for each of the three categories (not-vaccinated, partially vaccinated, fully vaccinated)? [Example: what is the probability of ending up in Intensive Therapy, conditional on being a 40-59 non-vaccinated?]