Finding Unconditional Probability from Conditional Probabilities Example

Example

• With $2\%$ chance of people from sample space having disease Hepatitis ($HB$)
• With a test that provides:
  • $P(+|HB)=0.96$
  • $P(+|H{B}^{\prime })=0.02$
• Then, we find the $P(+)$

Soln

• $P(+)=P(+|HB)\ast P(HB)+P(+|H{B}^{\prime })\ast P(H{B}^{\prime })$
• $⟹P(+)=0.96\ast 0.02+0.02\ast 0.98$
• $⟹P(+)=0.0388$