Answer to Question #152321 in Statistics and Probability for Yosef

Question

In case of headache, 3 patients out of 5 take Panadol while 2 out 5 take another medication M. 75% of patients feel better knowing that they took Panadol. 90% feel better given they took the other medication

1. What is the probability of having no longer a headache? 2. What is the probability that a patient feels better given he took Panadol?

Answer 1

Let $A$ be the event "patient takes Panadol", $B$ be the event "patient takes another medication M", and $C$ be the event "patient feels better".

Given that

$P(A)=\dfrac{2}{5}=0.4, P(B)=\dfrac{3}{5}=0.6,$

$P(C|A)=0.75, P(C|B)=0.90$

1. By the theorem of total probability 

$$P(C)=P(C|A)P(A)+P(C|B)P(B)$$

$$=0.75(0.4)+0.90(0.6)=0.84$$

The probability of having no longer a headache is $0.84.$

2.

$$P(C|A)=0.75$$

The probability that a patient feels better given he took Panadol is $0.75.$