An air quality measurement station measures levels of $\mathrm { NO } _ { 2 }$ and suspended particles. The probability that on a given day a level of $\mathrm { NO } _ { 2 }$ exceeding the permitted level is measured is 0.16. On days when the permitted level of $\mathrm { NO } _ { 2 }$ is exceeded, the probability that the permitted level of particles is exceeded is 0.33. On days when the level of $\mathrm { NO } _ { 2 }$ is not exceeded, the probability that the level of particles is exceeded is 0.08.\ a) ( 0.5 points) What is the probability that on a given day both permitted levels are exceeded?\ b) ( 0.75 points) What is the probability that at least one of the two is exceeded?\ c) ( 0.5 points) Are the events ``on a given day the permitted level of $\mathrm { NO } _ { 2 }$ is exceeded'' and ``on a given day the permitted level of particles is exceeded'' independent?\ d) ( 0.75 points) What is the probability that on a given day the permitted level of $\mathrm { NO } _ { 2 }$ is exceeded, given that the permitted level of particles has not been exceeded?