Science:Math Exam Resources/Courses/MATH103/April 2011/Question 05 (c)
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Question 05 (c) 

In a room two different lightbulbs and are installed. According to the packaging, lightbulb fails before time with probability ( in months). Lightbulb has a probability density function for the failure time given by What is the probability that both lightbulbs are still working after months? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

A light bulb is still working after months if and only if it has not failed before months. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The probability that lightbulb is still working after months is equal to the probability that it has not failed before months, which is The probability that lightbulb is still working after months is equal to the probability that it fails at a time greater than :
The probability that both lightbulbs are still working after months is equal to the product of the two probabilities found above, which is
