Data Model and Decision Making
|Homework: | DATA MODEL AND DECISION MAKING by Demitri Betrimas |
• Exercise 2.4 • Exercise 2.9 • Exercise 2.24
Exercise 2.4 – a) What is the probability of finding oil at all three of the sites? The table below shows the different events and there probabilities Event Symbol Probability The event of finding oil at 1st site A 0.70 The event of finding oil at 2nd site B 0.85 The event of finding oil at 3rd site C 0.80 Since all three events are independent and does not affect the outcome of the other so the probability of finding oil at all three sites can be known by applying “Implication of fourth law of probability” P (A and B and C) = P (A) * P (B) * P(C) = 0.70 * 0.85 * 0.80 = 0.476 b) What is the probability of not finding oil at any of the three sites? Probability of NOT finding oil at event A= 1– 0.70 = 0.30 Probability of NOT finding oil at event A= 1– 0.85 = 0.15 Probability of NOT finding oil at event A= 1– 0.80 = 0.20 So Probability of not finding all oil at any sites is P(Not A and Not B and Not C ) = P(Not A) * P(Not B) * P(Not C) = 0.30 * 0.15 * 0.20 = 0.009
Exercise 2.9 – a) For constructing the probability table let us presume that
H – denote the event that person is Infected with HIV
V – denote the event that person is NOT infected with HIV
Y – denote the event that person is Tested positive in the Blood test
N – denote the event that person is Tested negative in the Blood test
Other data provided to us in the question is
Total people infected with HIV – 550,000 (0.55 mil)
Drug user with HIV infection – 275,000 (0.275 mil)
Remaining with HIV infection – 275,000 (0.275 mil)
Total drug user – 10 mil
Total US population – 250 mil
Probability of any person being infected by HIV P(H) =
• Exercise 2.4 • Exercise 2.9 • Exercise 2.24
Exercise 2.4 – a) What is the probability of finding oil at all three of the sites? The table below shows the different events and there probabilities Event Symbol Probability The event of finding oil at 1st site A 0.70 The event of finding oil at 2nd site B 0.85 The event of finding oil at 3rd site C 0.80 Since all three events are independent and does not affect the outcome of the other so the probability of finding oil at all three sites can be known by applying “Implication of fourth law of probability” P (A and B and C) = P (A) * P (B) * P(C) = 0.70 * 0.85 * 0.80 = 0.476 b) What is the probability of not finding oil at any of the three sites? Probability of NOT finding oil at event A= 1– 0.70 = 0.30 Probability of NOT finding oil at event A= 1– 0.85 = 0.15 Probability of NOT finding oil at event A= 1– 0.80 = 0.20 So Probability of not finding all oil at any sites is P(Not A and Not B and Not C ) = P(Not A) * P(Not B) * P(Not C) = 0.30 * 0.15 * 0.20 = 0.009
Exercise 2.9 – a) For constructing the probability table let us presume that
H – denote the event that person is Infected with HIV
V – denote the event that person is NOT infected with HIV
Y – denote the event that person is Tested positive in the Blood test
N – denote the event that person is Tested negative in the Blood test
Other data provided to us in the question is
Total people infected with HIV – 550,000 (0.55 mil)
Drug user with HIV infection – 275,000 (0.275 mil)
Remaining with HIV infection – 275,000 (0.275 mil)
Total drug user – 10 mil
Total US population – 250 mil
Probability of any person being infected by HIV P(H) =