Answer:
a) 0.5348
b) 0.2064
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
