The probability that a person selected at random from a populetion wil

gabioskay7

gabioskay7

Answered question

2021-11-13

The probability that a person selected at random from a populetion will exhibit the classic symptom of a certain disease is 0.2, and the probability that aperson selected at random has the disease is 0.23. The probability that a person who has the symptom also has the disease is 0.18. If a person is chosen at random from the population and does not have the symptom, what is the likelihood that the person has the disease?

Answer & Explanation

Louise Eldridge

Louise Eldridge

Beginner2021-11-14Added 17 answers

Step 1
Probability quantifies the chances of happening an event. The probability values always lie in the range 0 and 1.
An event is a subset of the sample space. Sample space consist the set of all possible outcomes and the probability of sample space is 1. Conditional probability is the probability of occurrence of an event with some association with other events.
Step 2 Let S be the event that randomly selected person has symptom and D be the event that a randomly selected person has a disease. Then P(SD) indicates the probability that an randomly selected person shown symptom and has disease. It is given that P(S)=0.2, P(D)=0.23, P(SD)=0.18.
The complement of S indicates that a randomly selected person does not have symptoms, that is P(Sc)=1P(S)=0.8. Then,
P(DSc)=P(D)P(SD)
=0.230.18
=0.5
The conditional probability P(DSc) indicates the probability that a randomly selected person has disease given does not have any symptoms. This is calculated below.
P(DSc)=P(DSc)P(Sc)
=0.050.8
=0.0625
So 0.0625 is the required probability.

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