The company type and risk level are not independent events
Probability of moderate to high risk given that firm is aerospace
This is calculated using:
P(Moderate to High risk | Aerospace) = n(Moderate to High risk and Aerospace)/n(Aerospace)
Using the table of values, we have:
P(Moderate to High risk | Aerospace) = 15/(23+15)
Evaluate
P(Moderate to High risk | Aerospace) = 0.3947
Hence, the probability is 0.3947
Probability of moderate to high risk given that firm is Food retailer
This is calculated using:
P(Moderate to High risk | Food retailer) = n(Moderate to High risk and Food retailer)/n(Food retailer)
Using the table of values, we have:
P(Moderate to High risk | Food retailer= 16/(18+16)
Evaluate
P(Moderate to High risk | Food retailer= 0.4706
Hence, the probability is 0.4706
Determine if the company type and risk level are independent
Using the table of values, we have:
P(Aero | Low) = 23/(23 + 18)
P(Aero | Low) = 0.5610
And, we have:
P(Aero) = 23/(23 + 15 + 18 + 16)
P(Aero) = 0.3194
Both probabilities are not equal
Hence, the company type and risk level are not independent
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