Question

The probability that a person with certain symptoms has hepatitis is 0.75. The blood test used to confirm this diagnosis gives positive results for 86?% of people with the disease and 5?% of those without the disease. What is the probability that an individual who has the symptoms and who reacts positively to the test actually has? hepatitis?

Answer 1

Answer:

0.981

Step-by-step explanation:

We have to find the probability that an individual who has the symptoms and who reacts positively to the test has hepatitis

Let $E_1$be the event that denotes the symptoms has hepatitis and $E_2$ denotes the symptoms have not hepatitis

Let A be the event the denotes the blood test result positive  

We have to find the value of $P(E_1/A)$

We have $P(E_1)=0.75$

$P(E_2)=1-0.75=0.25$

$P(A/E_1)=86%=0.86$

$P(A/E_2)=5%=0.05$

Using formula

$P(E_1/A)=\frac{P(E_1)\times P(A/E_1)}{P(E_1)\cdotP(A/E_1)+P(E_2)\cdotP(A/E_2}$

Substitute the values in the given formula

Then,we get

$P(E_1/A)=\frac{0.75\times .86}{0.75\times0.86+0.25\times 0.05}$

$P(E_1/A)=\frac{0.645}{0.6575}=0.9809$

$P(E_1/A)=0.981$

Hence, the probability that an individual who has the symptoms and who reacts positively to the test actually has hepatitis =0.981