Question

A manufacturer is producing face masks and PPEs for use by the DOH for its frontliners to be protected from COVID-19 in different hospitals nationwide.  

Alternative	S1	S2	S3	S4
Probability	0.35	0.25	0.25	0.15

The manufacturers want to get the services of the research agency. The research agency offers its services to the manufacturer at a cost of PhP750,000 and provides a positive or a negative report. Based on the past experiences of the research agency, it mentioned that the probability of a positive report given S1 is 0.40 and probability of negative report given S3 is 0.30 and probability of negative report given S4 is 0.70.

a) Assuming that the probability of negative report is 0.49, what will be the probability of S1 given negative report. Answer in figure only and round off to 4 decimal places.

b) Given the data in the problem and in (a), determine the probability of S4 given positive report. Answer in 4 decimal places.

Answer 1

the sum of probability of the all the event is =1

here s1 = 0.35 , s2 = 0.25 , s3 = 0.25 , s4 =0.15

the probability of negative report is 0.49 so probablity of positive will be 0.51 by the question given in a) statement.

so ans for a ) 0.4285

for b) 0.0882