1) The probability of getting a certain disease is 0.2. A certain test is available which returns a positive result 90% of the time for those with the disease, and a negative result 75% of the time for those without the disease. Compute Pr{Test positive}. (Hint: It may be helpful to draw a probability tree, and round to two decimal place)
2) The probability of getting a certain disease is 0.2. A certain test is available which returns a positive result 90% of the time for those with the disease, and a negative result 75% of the time for those without the disease. Compute Pr{Test negative}. (Hint: It may be helpful to draw a probability tree, and round to two decimal places)
3) The probability of getting a certain disease is 0.2. A certain test is available which returns a positive result 90% of the time for those with the disease, and a negative result 75% of the time for those without the disease. Compute Pr{Test positive | No disease}. (Hint: It may be helpful to draw a probability tree, and round to two decimal places)
Please show work so I can do the rest!
Thank you!
0.2/0.8=0.25 for test positive/nodisease
I've got .39 for test positive, .61 for the negative test and .61 for the test positive/no disease but they were all marked as wrong so I was wondering if someone could help me with these questions? I used probability tree to find the right answers but it's clear that I think I am missing out something.
Thank you so much!
OK!!!
Test Positive = .38
Test Negative = .62
Test Positive/no disease = ????
I've got the first two right but the 3rd one is still messing me up!
To solve these problems, we can use a probability tree to calculate the probabilities step by step. Let's start by drawing the tree for Problem 1:
1) Probability of getting the disease: 0.2 (Disease)
Probability of not getting the disease: 0.8 (No disease)
Disease (0.2) No disease (0.8)
| |
Test positive (0.9) Test negative (0.1) Test negative (0.75) Test positive (0.25)
| | | |
Outcome: TP Outcome: FN Outcome: TN Outcome: FP
Now, let's calculate the probabilities:
1) Pr{Test positive}:
To find this probability, we need to consider the two possible outcomes when the test is positive: either the person has the disease and the test is true positive (TP), or the person doesn't have the disease but the test is a false positive (FP).
Pr{Test positive} = Pr{TP} + Pr{FP}
Pr{TP} = Pr{Disease} * Pr{Test positive | Disease} = 0.2 * 0.9 = 0.18
Pr{FP} = Pr{No disease} * Pr{Test positive | No disease} = 0.8 * 0.25 = 0.2
Pr{Test positive} = 0.18 + 0.2 = 0.38
So, the probability of getting a positive result from the test is 0.38 (rounded to two decimal places).
Now, let's move on to Problem 2:
2) Pr{Test negative}:
To find this probability, we need to consider the two possible outcomes when the test is negative: either the person has the disease but the test is a false negative (FN), or the person doesn't have the disease and the test is true negative (TN).
Pr{Test negative} = Pr{FN} + Pr{TN}
Pr{FN} = Pr{Disease} * Pr{Test negative | Disease} = 0.2 * 0.1 = 0.02
Pr{TN} = Pr{No disease} * Pr{Test negative | No disease} = 0.8 * 0.75 = 0.6
Pr{Test negative} = 0.02 + 0.6 = 0.62
So, the probability of getting a negative result from the test is 0.62 (rounded to two decimal places).
Finally, let's solve Problem 3:
3) Pr{Test positive | No disease}:
To find this probability, we only need to consider the outcome where the person doesn't have the disease (No disease) and the test is positive (Test positive).
Pr{Test positive | No disease} = Pr{No disease} * Pr{Test positive | No disease} = 0.8 * 0.25 = 0.2
So, the probability of getting a positive result from the test given that the person doesn't have the disease is 0.2.
You can now use this information to calculate the rest of the probabilities or solve similar problems.