Q. No. 1a) An urn contains 5 black balls, 6 red balls, and 3 white balls. Four b
ID: 2914402 • Letter: Q
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Q. No. 1a) An urn contains 5 black balls, 6 red balls, and 3 white balls. Four balls are drawn in succession each ball being replaced after the next one is drawn. What is the probability that the first ball is red, the second white and the third black. b) In a factory machine A produces 70% of the output and machine B produces 30%. On the average 8 items in 1000 produced by A are defective and 5 items in 1000 produced by B are defective. An item drawn at random from a day’s output is defective. What is the probability that it was produced by A or B?Explanation / Answer
1a) An urn contains 5 black balls, 6 red balls, and 3 whiteballs. Four balls are drawn in succession each ball being replaced after the next one is drawn. What is the probabilitythat the first ball is red, the second white and the thirdblack. There are a total of 14 balls. The first one is red sowe have a P of 6 / 14. Ball # 1 is not replaced until afterball #2 is removed. The P of ball #2 being white is 3 / 13. Ball #1 is now put back and ball #2 is kept out. The Pof ball #3 being black is 5 / 13. Multiply these together: (6 / 14)*(3 / 13)*(5 / 13) = 45 / 1183 = .03803888 b) In a factory machine A produces 70% of the output andmachine B produces 30%. On the average 8 items in 1000 produced by A are defective and 5 items in 1000 producedby B are defective. An item drawn at random from aday’s output is defective. What is the probability that it wasproduced by A or B? Say the total output is 10,000 in a day. Machine Aproduced 7000 with 7 * 8 or 56 defects. Machine B produced3000 with 3 * 5 or 15 defects. There were a total of 71defects. So the p of a given defective item coming from A is56 / 71 or .788732 and the p of the defective item coming from B is 15 / 71 =.211268 Hope this helps!Related Questions
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