Hi there!
We can begin by multiplying by its conjugate:
Simplify using the identity:
Take the square root of the expression:
Multiply again by the conjugate to get a SINGLE term in the denominator:
Simplify:
Use the above trig identity one more:
Cancel out sinA:
Split the fraction into two:
Recall:
Simplify:
Answer:
The probability a person selected random is not suffering from Malaria is 0.725.
Step-by-step explanation:
Denote the events as follows:
X = a person is suffering from Malaria
M = a man
W = a woman
The information provided is:
P (M) = P (W) = 0.50
P (X|M) = 0.10
P (X|W) = 0.45
Compute the probability a person selected random is suffering from Malaria as follows:
Then the probability a person selected random is not suffering from Malaria is:
P (X') = 1 - P (X)
= 1 - 0.275
= 0.725