A site consists of 60 sand and 40 silt in separate layers an

A site consists of 60% sand and 40% silt in separate layers and pockets. At this site, 10% of
sand samples and 5% of silt samples are contaminated with trace amounts of arsenic. If a
soil sample is selected at random, what is the probability that it is a contaminated sample?
Also, if a soil sample was contaminated, what is the probability that the soil type is silt?

Solution

ANS:- TOTAL SAND SAMPLE AT SITE=60%=0.6  

CONTAMINATED SAND SAMPLE=10%=0.1

TOTAL SILT SAMPLE AT SITE=40%=0.4

CONTAMINATED SILT SAMPLE AT SITE=5%=0.05

PROBABILITY OF GETTING CONTAMINATED SAND SAMPLE=0.6*0.1=0.06

PROBABILITY OF GETTING CONTAMINATED SILT SAMPLE=0.4*0.05=0.02

PROBABILITY OF CONTAMINATED SAMPLE=0.06+0.02=0.08 ANS.

IF A SOIL SAMPLE WAS CONTAMINATED, THEN PROBABILITY OF TYPE OF SOIL IS SILT=(0.02)/(0.02+0.06)=0.25=25% ANS