Question

A shelf in the Metro Department Store contains 95 colored ink cartridges for a popular ink-jet printer. Five of the cartridges are defective.
(a) If a customer selects 3 cartridges at random from the shelf, what is the probability that they are all defective? (Round your answer to five decimal places.)

(b) If a customer selects 3 cartridges at random from the shelf, what is the probability that at least 1 is defective? (Round your answer to three decimal places.)

Answer 1

from 95, 5 are defective, so what is the probability of finding 1 defective cartridge ?

Answer 2

5/95, so 1/19

Answer 3

right, now we need to find that all 3 cartridge are defective, so first lets find when 2 are chosen and both are defective, what is the probability for this? any ides ?

Answer 4

(5/95)*(4/94) maybe?

Answer 5

absolutely correct!
so now, in same way, what about 3?

Answer 6

(5/95)*(4/94)*(3/93) so 0.000072?

Answer 7

yup.

Answer 8

to 5 decimal places it would only be 0.00007.

Answer 9

Awesome. The second part of the question is actually pick 2 not pick 3, and at least one is defective. Would that be (5/95) * (1/94) ?

Answer 10

had it been 3, it would have been really easy.
to get the probability of atleast 1 defective, you first find the probability that none of them are defective.

Answer 11

None are defective is 90/95, defective is 5/95

Answer 12

i meant none of the 2 are defective, so 90/95 multiplied by what ?

Answer 13

(90/95)*(89/94)

Answer 14

correct, now use this
P(atleast 1) = 1- P(none)

Answer 15

so 1- product of those 2 will give u probability of atleast 1

Answer 16

u there ? did u understand that ?

Answer 17

A little, I'm trying to figure it out and write it out but I'm getting confused. Is it 1-(5/95)/(90/95)?

Answer 18

nopes, its 1- (90/95)*(89/94).
just use this when u want to find the probability of ATLEAST 1.
P(ATLEAST 1) = 1- P(NONE)

Answer 19

Oh! Ok so it's..... one sec I'm going to bust out my calculator

Answer 20

me too :P

Answer 21

I'm doing this completely wrong, I'm sorry.

Answer 22

why? what happened ?

Answer 23

Trying to find pick two at least one is defective. So for the one that IS defective it is 5/95 and for the second one that can be either defective or normal, would that be 1/94? I don't understand why there is (90/95)*(89/94). Shouldn't it just be (5/95)*(1/94)?

Answer 24

But that isn't right and I don't understand why.

Answer 25

just a sec, let me think...

Answer 26

'for the second one that can be either defective or normal, would that be 1/94'<--NO
we are first finding the probability that when 2 are selected, BOTH of them are NOT defective. what is that probability ?

Answer 27

90/95 * 89/94.

Answer 28

u clear with this, right ?
now to find the probability that atleast one of the cartridge is defective, we do
1-probability that both (all) the cartridges are NOT defective.

Answer 29

Ok, so that would be 0.10302. I can understand that sort of.

Answer 30

yeah, thats correct.

Answer 31

just remember this : P(ATLEAST 1) = 1- P(NONE)

Answer 32

so that would be 5/95 = 1-90/95 * 89/94 ?

Answer 33

Oh nevermind, that is just x = 1-90/95 * 89/94

Answer 34

Yes!! That's right! Thank you so much!!

Answer 35

welcome ^_^ and
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