Question

) P(Has Condition)=

6) P(Tested Negative)=

7) P(has condition| tested positive)=

8) P(has condition
tested positive)=

9) P(has condition
tested positive)=

10) P(has condition
tested negative)=

11) P(does not have condition| tested negative)=

Answer 1

I don't see the underlying numbers (prevalence, sensitivity, specificity or a table). Below I give the general formulas you need and a worked numeric example so you can map them to your problem.

Notation
- p = P(Has condition) (prevalence)
- Se = sensitivity = P(test+ | Has)
- Sp = specificity = P(test− | No condition)
- No = 1 − p = P(Does not have condition)

Formulas
1) P(Has condition) = p

6) P(Tested negative) = P(test−) = P(test− | Has)P(Has) + P(test− | No)P(No)
= (1 − Se)·p + Sp·(1 − p)

7) P(Has condition | tested positive) = P(Has | test+) = Se·p / [Se·p + (1 − Sp)·(1 − p)]

8) P(Has condition and tested positive) = P(Has ∧ test+) = Se·p

9) (If this duplicates 7) same as 7; if it means joint probability it's same as 8

10) P(Has condition and tested negative) = P(Has ∧ test−) = (1 − Se)·p

11) P(Does not have condition | tested negative) = P(No | test−) =
Sp·(1 − p) / P(test−) where P(test−) is from line 6.

Worked example
Let p = 0.05 (5% prevalence), Se = 0.90, Sp = 0.95.
- 1) P(Has) = 0.05
- 6) P(test−) = (1−0.90)·0.05 + 0.95·0.95 = 0.005 + 0.9025 = 0.9075
- 7) P(Has | test+) = 0.90·0.05 / (0.90·0.05 + 0.05·0.95)
= 0.045 / 0.0925 ≈ 0.4865 (48.65%)
- 8) P(Has ∧ test+) = 0.90·0.05 = 0.045
- 10) P(Has ∧ test−) = (1−0.90)·0.05 = 0.005
- 11) P(No | test−) = 0.9025 / 0.9075 ≈ 0.9945 (99.45%)

If you provide the prevalence, sensitivity and specificity (or a 2×2 table of counts), I can plug them in and give the exact values for your case.