Answer:
0.9586
Step-by-step explanation:
From the information given:
7 children out of every 1000 children suffer from DIPG
A screening test designed contains 98% sensitivity & 84% specificity.
Now, from above:
The probability that the children have DIPG is:
[tex]\mathbf{P(positive) = P(positive \ | \ DIPG) \times P(DIPG) + P(positive \ | \ not \DIPG)\times P(not \ DIPG)}[/tex][tex]= 0.98\imes( \dfrac{7}{1000}) + (1-0.84) \times (1 - \dfrac{7}{1000})[/tex]
= (0.98 × 0.007) + 0.16( 1 - 0.007)
= 0.16574
So, the probability of not having DIPG now is:
[tex]P(not \ DIPG \ | \ positive) = \dfrac{ P(positive \ | \ not DIPG)\timesP(not \ DIPG)} { P(positive)}[/tex]
[tex]=\dfrac{ (1-0.84)\times (1 - \dfrac{7}{1000}) }{ 0.16574}[/tex]
[tex]=\dfrac{ 0.16 ( 1 - 0.007) }{0.16574}[/tex]
= 0.9586
