Question

a) What is the probability that a random participant will have a negative blood test?   b) If a randomly selected participant has a positive blood test, what is the probability that they do not have lockjaw?

Answer 1

a) 0.5348

b) 0.2064

Step-by-step explanation:

We can represent the situation with the following diagram

Then, the probability that a participant will have a negative blood test can be calculated as:

P(N) = P(L)P(N/L) + P(L')P(N/L')

P(N) = 0.52(0.29) + 0.48(0.80)

P(N) = 0.5348

On the other hand, the probability that a participant do not have lockjaw given that it has a positive blood test is calculated as:

P(L'/P) = P(L' and P)/P(P)

Where

P(P) = 0.52(0.71) + 0.48(0.2)

P(P) = 0.4652

and

P(L' and P) = (0.48)(0.2)

P(L' and P) = 0.096

So,

P(L'/P) = 0.096/0.4652

P(L'/P) = 0.2064

Therefore, the answers are

a) 0.5348

b) 0.2064