There are five urns, numbered 1 to 5. Each urn contains 10 balls. Urn k has k de
ID: 3041953 • Letter: T
Question
There are five urns, numbered 1 to 5. Each urn contains 10 balls. Urn k has k defective balls and 10 k nondefective balls, k = 1, 2, . . . , 5. For example, urn 3 has three defective balls and seven nondefective balls. Consider the following random experiment: First an urn is selected at random, and then a ball is selected at random from the selected urn.
a) What is the probability that a defective ball will be selected ?
b) If we have already selected the ball and noted that it is defective, what is the probability that it came from urn 5 ?
Explanation / Answer
a)P(defective ball)=P(urn 1 and defective ball+urn 2 and defective ball+urn 3 and defective ball+urn 4 and defective ball+urn 5 and defective ball)=(1/5)*(1/10)+(2/5)*(1/10)+(1/5)*(3/10)+(1/5)*(4/10)+(1/5)*(5/10)=15/50=3/10 =0.3
b) probability that it came from urn 5 given defective ball =P(urn 5 and defective ball)/P(defective ball)
=(1/5)*(5/10)/(0.3)=1/3 =0.3333
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