Question

There are five (5) urns and they are numbered 1-5, each urn contains 10 balls. Uni has i defective and 10-i non-defective balls (i = 1, 5). An urn is chosen at random and then a ball is drawn from the chosen urn, the experiment does not know which of the urns was selected (i) What is the probability that a defective ball is drawn (ii) If the ball drawn turns out to be defective, what is the probability that it comes from urn i=5​

Answer 1

Step-by-step explanation:

(i) The probability that a defective ball is drawn is equal to the total number of defective balls divided by the total number of balls. In this case, there are a total of 5 defective balls (one in each urn) and a total of 50 balls (10 in each urn), so the probability of drawing a defective ball is 5/50 = 1/10.

(ii) If the ball drawn turns out to be defective, the probability that it comes from urn i=5 is equal to the number of defective balls in urn 5 divided by the total number of defective balls. In this case, there is only 1 defective ball in urn 5 and a total of 5 defective balls, so the probability that a defective ball drawn comes from urn 5 is 1/5.

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