Stats-crv-exponential distribution

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The discussion revolves around calculating probabilities related to the failure of light bulbs with a mean time to failure of 5000 hours. The first part of the problem involves finding the probability that a light bulb is still functioning after 10,000 hours, which is calculated as approximately 0.1353. The second part requires determining the probability that at least one out of five light bulbs remains operational after the same duration. To solve this, one must consider the complementary probability of none working, which involves calculating the inverse scenario. The thread emphasizes the need for clarity in applying probability concepts to derive the correct answers.
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Homework Statement



The time to failure for a certain light bulb in constant failure rate mode has a mean time to failure of 5000 hours.

What is the probability that a randomly chosen light bulb is still burning after 10,000 hours? Give answer to 4 decimals.

If 5 light bulbs are installed in different street lamps along Main Street, what is the probability that at least 1 will be working after 10,000 hours? Give answer to 4 decimals.


The Attempt at a Solution


I believe the first part would simply be e-(1/5000*10000)=.1353

The second part I am at a loss on how to solve it.
 
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