Problem 2: Fifteen parts are examined for defects. It is found that 10 are good,

ID: 2946575 • Letter: P

Question

Problem 2: Fifteen parts are examined for defects. It is found that 10 are good, 3 have minor defects, and 2 have major defects. (a) What is the probability that a randomly selected one part is good? (b) Two parts are chosen at random from the 15 without replacement, that is, the first part chosen is not returned to the mix before the second part is chosen. Notice, then, that there will be only 14 possible choices for the second part. (i) What is the probability that both are good? (i) What is the probability that exactly one part has a major defect? (You may use the tree diagram to find out all possible outcomes)

Explanation / Answer

Ans a) For one randomly selected part to be good it has to be picked up from the 10 which are good so there are 10 ways in which a good part can be choosen and in total there are 15 ways of choosing a part

So Probability that a randomly selected part is good = Number of Favourable ways / Total number of ways = 10 /15 = 0.667

Ans b) We need to calculate the number of ways for any outcome

So choosing 2 out of 10 good parts can be done in 10 ways for the first draw and 9 ways for the second draw so the required number of ways = 10 * 9 = 90 ways

And the total ways of selecting 2 parts is 15*14 = 210 ways

Therefore Probability that both are good is = 90/210 = 0.4286

Ans ii) So it has two cases

The first one is major defect

For this we need to take one from the 2 major defect first that is in 2 ways and then take 1 from the 13 which are not major defect so total number of ways is 2 * 13 = 26

And second case is that the 2nd pick is major defect

So first pick can be in 13 ways for the 13 parts which are not major defect and the 2nd one in 2 ways to pick one from the 2 major defects. So total number of ways = 26

So total number of ways for which exactly one major defect is 52.

Therefore probability of exactly one major defect is 52/210 = 0.2476

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Problem 2: Fifteen parts are examined for defects. It is found that 10 are good,

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Problem 2: Fifteen parts are examined for defects. It is found that 10 are good,

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