On Chicago PD, detectives Halstead and Ruzek are the sharpshooters. Halstead\'s

Question

On Chicago PD, detectives Halstead and Ruzek are the sharpshooters. Halstead's chance of hitting a target is 72 and Ruzek's is 67. What is the probability that exactly one of them hits their target? Dexter hunts the most evil people in Miami. He spends 9 hours hunting law enforcement personnel, 5 hours hunting government officials, 3 hours hunting drug dealers, and 1 hour hunting serial killers. Based on past experience, he thinks he will be successful for law enforcement, government officials, drug dealers, and serial killers with probabilities of 15, 20, 25, and 40 respectively. Calculate the expected value, variance, and standard deviation of the hours spent hunting.

Explanation / Answer

7.

We are given that P[Halsted hits the target] = 0.72 & P[Ruzek hits the target] = 0.67

Required probability = P[Exactly one of them hits the target] = P[Halstead hits but Ruzek does not] + P[Ruzek hits but Halstead does not] = 0.72*0.33 + 0.28*0.67 = 0.4252

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