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3.The following are real data from Santa Clara County, CA. As of a
certain time, there had been a total of 3,059 documented cases of
AIDS in the county. They were grouped into the following categories:

Homosexual IV Drug User* Heterosexual Contact Other
Female 0 70 136 49
Male 2,146 463 60 135

Suppose a person with AIDS in Santa Clara County is randomly
selected.
(i) Find P (Person is female). (2 Marks)
(ii) Find P (Person has a risk factor heterosexual contact). (2 Marks)
(iii) Find P (Person is female OR has a risk factor of IV drug user (2 Marks)
(iv) Find P (Person is female AND has a risk factor of homosexual) (2 Marks)
(v) Find P (Person is male AND has a risk factor of IV drug user) (2 Marks)
(vi) Find P (Person is female GIVEN person got the disease from
heterosexual contact) (2 Marks)
(v)Construct a Venn diagram. Make one group females and
the other group heterosexual contact. (3 Marks)

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  • I) the probability that the person is female is 8.33%.
  • II) the probability that the person has a risk factor heterosexual contact is 6.40%.
  • III) the probability that the person is female or has a risk factor of IV drug user is 23.47%.
  • IV) the probability that the person is female and has a risk factor of homosexual is 0%.
  • V) the probability that the person is male and has a risk factor of IV drug user is 15.13%.
  • VI) the probability that the person is female given that the person got the disease from heterosexual contact is 69.38%.

Given the data mentioned in the table, the following calculations must be performed to obtain the requested probabilities:

I.-

(0 + 70 + 136 + 49) / (2,146 + 463 + 60 + 135 + 0 + 70 + 136 + 49) = X

255/3059 = X

0.0833 = X

II.-

196/3059 = X

0.0640 = X

III.-

(255 + 463) / 3059 = X

718/3059 = X

0.2347 = X

IV.-

0/3059 = X

0 = X

V.-

463/3059 = X

0.1513 = X

VI.-

136/196 = X

0.6938 = X

Therefore, I) the probability that the person is female is 8.33%, II) the probability that the person has a risk factor heterosexual contact is 6.40%, III) the probability that the person is female or has a risk factor of IV drug user is 23.47%, IV) the probability that the person is female and has a risk factor of homosexual is 0%, V) the probability that the person is male and has a risk factor of IV drug user is 15.13%, and VI) the probability that the person is female given that the person got the disease from heterosexual contact is 69.38%.

Learn more about maths in https://brainly.com/question/25815188

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