Question

Try this one:

There are \(100\) transistors in a box of which some are defective. At random, two transistors are consecutively taken out without replacement. A scientist wants to know the chances of exactly one of them being good and the other being defective. What number of defective transistors takes this chance below \(30 \% \)?

Answer 1

15... :/

Answer 2

Not that hard, give it a quick try guys!!

Answer 3

I am sorry saso, that is not the correct answer.

Answer 4

is the answer above that number or below? more or less...

Answer 5

above, more than the double of that number actually.

Answer 6

35

Answer 7

Is the chance of it being defective 30%?

Answer 8

no, only below.

Answer 9

hmmm seems harder than i thought

Answer 10

i don't know how to solve this but i'm trying to use logic to find my way out... i need a couple more hints to know if i'm close to the answer... you mind helping me out?

Answer 11

sure I would love to, where are you stuck ?

Answer 12

i copied what i was typing to the clipboard, i'll paste it later, i'm being called. brb

Answer 13

sure.

Answer 14

Let d be the number of defective transistors.

probability of being defective is d/n, where n is remaining transistors
probability of being good is (100-d)/n, where n is remaining transistors

There are 2 possibilities, either the 1st transistor is good or it is defective and the 2nd is the opposite

\[P = \frac{d}{100}*\frac{100-d}{99} + \frac{100-d}{100}*\frac{d}{99}\]
\[P = \frac{2d(100-d)}{9900}\]
set P = 0.3 and solve for d
\[0.3 > \frac{2d(100-d)}{9900}\]
\[1485 > 100d-d^{2}\]
\[d^{2} -100d +1485 > 0\]
\[d < 18.14\]
\[d>81.86\]

Answer 15

i think the above statements make sense, the early parts falls within the logic i was trying to construct but the figures are different... oh well :)