GATE Overflow Test Series | Mixed Subjects | Test 3 | Question: 20

Question

Assume that a light bulb lasts on average $100$ hours. Assuming exponential distribution, the probability that it lasts either more than $200$ hours or not more than $50$ hours is __________. (Rounded to $2$ decimal points)

Answer 1

Probability that the bulb lasts either more than $200$ hours or less than $50$ hours.  $P = P(x > 200) + P( x \leq 50)$

$\qquad  =  P(x >  200) + 1 - P( x > 50)$

$\qquad  = e^{-200\lambda}  + 1 - e^{-50 \lambda}$

Here, $\lambda = \frac{1}{100}.$

So, $P = e^{-2}  + 1 -  e^{-0.5} =0.5288$