Probability question!?

Posted on 2015-09-03 13:29:00 in Math by TUFFEL

A crime was committed on an island. Witnesses all agree that the criminal was driving a blue motorbike and had blond hair, and they also smoked. Police determine that 1 in 50 motorbikes on the island are green, 30 percent of residents smoke and 20 percent have blond hair. The next day the police see a green motorbike whose rider is blond and smoking a cigarette, they arrest the person for the crime.

a) Assuming they are independent traits, what proportion of motorbike owners would fit this description?

b) If there are 10,000 motorbike owners on the island, estimate how many fit the description?

c) Assuming there is no other evidence, what is the probability that the suspect the police arrested is innocent of the crime?

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