Can someone please help me with this question on probability?! i got .68, is that right?!?

Question

A machine is powered by 3 similar batteries. It will only work if at least 2 of the batteries are working. P(any one battery breaks in less than 200hours)=.7. P(any one battery breaks in less than 100 hours)=.2. Find the probability the machine will work between 100 and 200 hours.

Answer 1

First of all work out the probability that it breaks down inside 100 hours:

P (all 3 break down in 100 hours) = .2 * .2 * .2 = 0.008
P (2 out of 3 break down in 100 hours) = 3 * .2 * .2 * .8 = 0.096
P(total < 100) = 0.104

Then work out the chance of it lasting BEYOND 200 hours

P (all 3 last > 200) = .3 * .3 * .3 = 0.027
P (2 out of 3 last > 200) = 3 * .3 * .3 * .7 = 0.189
P (total > 200) = 0.216

Therefore P (<100 or > 200) = 0.216 + 0.104 = 0.32
Therefore P(>100 and <200) = 1 - P(<100 or >200) = 0.68

You were right, well done.

Answer 2

WOW I cannot understand this can u explain this type of maths and what its called, I am interest. I am a disabled man of 50, this type of stuff really puzzles me with all these numbers and how u reach the answer. U kids of today have brains like computers, my respect goes out to you guys, the things u youngsters these days amaze me, well done and good luck on ur exams when they come, dont forget to write and explain what this is about, i would appreciate u doing so or anyone else.

Jimmy Essex England ( disabled gentleman )

Answer 3

Probability a battery works for less than 200 hours is 0.7, so probability it works for more than 200 hours is 0.3.

Probability at least two do not fail under 200 hours
F = fail, X = does not fail

FFF
FFX
FXF
FXX < 0.7*0.3*0.3 = 0.063
XFF
XFX < 0.3*0.7*0.3 = 0.063
XXF < 0.3*0.3*0.7 = 0.063
XXX < 0.3*0.3*0.3 = 0.027

0.063 + 0.063 + 0.063 + 0.027 = 0.216 chance of a machine failing after 200 hours

Probabilty at least two fail before 100 hours
F = fail, X = does not fail

FFF < 0.2*0.2*0.2 = 0.008
FFX < 0.2*0.2*0.8 = 0.032
FXF < 0.2*0.8*0.2 = 0.032
FXX
XFF < 0.8*0.2*0.2 = 0.032
XFX
XXF
XXX

0.008 + 0.032 + 0.032 + 0.032 = 0.104 chance of a machine failing before 100 hours

Chance of a machine not working between 100 and 200 hours
0.104 + 0.216 = 0.32

Probability the machine will work between 100 and 200 hours = 1 - 0.32 = 0.68

Answer 4

Hi Kate,
I got the answer 0.68 before i worked it out - instinctively !
you must be a cheeky monkey posing that question ! lol

Answer 5

Yes you are right! I worked it out the same way as gvih2g2 and came up with the same answer!!!

Answer 6

i got 567902553765788432...
but it might be slightly off.
sorry i tried but really cant do it, you must be a genius or sumink.