3. -/3 points DevoreStat9 2 E 034 My Notes Ask Your Teacher + Computer keyboard

Question

3. -/3 points DevoreStat9 2 E 034 My Notes Ask Your Teacher + Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 10 of which have electrical defects and 15 of which have mechanical defects. (a) How many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to order)? ways (b) In how many ways can a sample of 6 keyboards be selected so that exactly two have an electrical defect? ways (c) If a sample of 6 keyboards is randomly selected, what is the probability that at least 5 of these will have a mechanical defect? (Round your answer to four decimal places.) Need Help? Read tTalk to a Tutor

Explanation / Answer

(a) Selecting 6 keyboards out of 25 = 25C6 = 177,100 ways

(b) selecting 6 keboards where 2 have electrical defects.

So choose 2 out of 10 and 4 out of 15 = 10C2 * 15C4 = 45 * 1365 = 61,425 ways

(c) out of 6 keyboards chosen, at least 5 have mechanical defects.

At least 5 means (1 electrical defect + 5 mechanical defects) + (0 electrical defects + 6 mechanical defects)

= 10C1 * 15C5 + 10C0 * 15C6 = 10 * 3003 + 1 * 5005 = 30030 + 5005 = 35,035 ways

Total number of ways of selecting 6 keyboards = 25C6 = 177,100 ways

Therefore the required probability = 35035/177100 = 0.1978

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