464 Pollution control regulations A task force established b

4.64 Pollution control regulations. A task force established by the Environmental Protection Agency was scheduled to investigate 20 industrial firms to check for violations of pollution control regulations. However, budget cutbacks have drastically reduced the size of the task force. and they will be able to investigate only 3 of the 20 firms. If it is known that 5 of the firms are actually operating in violation of regulations, find the probability that a. None of the three sampled firms will be found in violation of regulations. b. All three firms investigated will be found in violation of regulations. . C. At least 1 of the 3 firms will be operating in violation of pollution control regulations.

Solution

N_total=total no of incident of choosing 3 out of 20 is ²⁰C₃ =1140

a) there is 5 industry not violating the rule

N_v0 = no of incident where all the three inductry is in nonviolating group is ⁵C₃ = 10

so probability of such event=⁵C₃/²⁰C₃ = 1/114

b) there is 15 industry violating the rule

N_v3 = no of incident where all the three inductry is in nonviolating group is ¹⁵C₃ = 455

so probability of such event=¹⁵C₃/²⁰C₃ = 91/228

c) no of incedent where atleat one is in violation is N_v1= N_total -N_v0

probability is N_v1/N_total = 137/228