Reliability question with exponential distribution

[alextsipkis]

Q. A certain type of memory chip is known to have an exponential life distribution with a failure rate of 0.15*10^-5.

a) What is the probability that a memory chip will survine 20,000 hours of use?

b) What is the probability it will fail in the next 35,000 hours if it has survived 20,000 hours of operation already??

c) By what time 10% of the chips , 50% of the chips, 63.2% of the chips be expected to fail??

I was wondering if somebody could help me with b OR c? Much appreciated. Please give some explanation , if possible, so easy for me to understand...

thanks.

 

[Valkarie]

a) The probability that a memory chip will survive 20,000 hours of use is 0.822.b) The probability it will fail in the next 35,000 hours if it has survived 20,000 hours of operation already is 0.176. This can be calculated by subtracting the probability of survival from 1, to get the probability of failure.c) By what time 10% of the chips, 50% of the chips, and 63.2% of the chips be expected to fail can be calculated using the formula for an exponential distribution: 10% failure rate: T = -ln(1-0.1)/0.000015 => T = 25,764 hours 50% failure rate: T = -ln(1-0.5)/0.000015 => T = 35,944 hours 63.2% failure rate: T = -ln(1-0.632)/0.000015 => T = 39,884 hours