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In a given sample studying corona virus infectiousness, 13% of infected people were youth and 66% were elderly
In a given sample studying corona virus infectiousness, 13% of infected people were youth and 66% were elderly. Moreover, of not infected people, 46% were adults and 11% were elderly. If you know that 73% of the sample received negative test result (i.e. not infected), and events are mutually exclusive and collectively exhaustive; Assume that infected and adult are two independent events, find the probability that a person is infected or adult? [5 points) b. Find the probability that a person is infected if he/she is an youth?
Expert Solution
Question 2) a) Percentage of negative sample (not infected) = 73% = 0.73
Percentage of people with positive sample (are infected) = 1-73% = 27% = 0.27
Percentage of people who are adults =
= Percentage of infected adults + Percentage of not infected adults
= (1-0.66-0.13)*0.27 + 0.46*0.73
= 0.3925
Percentage of people who are infected or adult =
= Percentage of people who are infected + Percentage of people who are adult - Percentage of people who are adult and infected
= 0.27 + 0.3925 - (0.27*0.21)
= 0.6058
Probability of people who are infected or adult are 0.6058.
b)Percentageof people who are youth =
= 0.27*0.13 + 0.73*(1-0.46-0.11)
= 0.27*0.13 + 0.73*0.43
= 0.349
Probability that a person is infected if he/she is a youth =
= Probability that a person is infected and is a youth / Probability that a person is a youth
= 0.13/0.349
= 0.3725.
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