SOLUTION: Find the probability that none of the 3 bulbs in a signal-light will have to be replaced during the first 1200 hours of operation if the lifetime X of the bulb is a random variable

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Question 364982: Find the probability that none of the 3 bulbs in a signal-light will have to be replaced during the first 1200 hours of operation if the lifetime X of the bulb is a random variable with the density f(x)=6[0.25-(x-1.5)^2] when 1<=x<=2, and f(x)=0 otherwise, where x is measured in multiples of 1000 hours.
Please show work if you know the aswer. =)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find P%281200%29=int%28f%28x%29%2Cdx%2C1%2C1.2%29
P%281200%29=int%28%286%281%2F4-%28x-3%2F2%29%5E2%29%29%2Cdx%2C1%2C1.2%29
P%281200%29=int%28%286%281%2F4-%28x%5E2-3x%2B9%2F4%29%29%29%2Cdx%2C1%2C1.2%29
P%281200%29=int%28%283%2F2-%286x%5E2-18x%2B27%2F2%29%29%29%2Cdx%2C1%2C1.2%29
P%281200%29=int%28%28-6x%5E2%2B18x-12%29%2Cdx%2C1%2C1.2%29
P%281200%29=-2%28%286%2F5%29%5E3-1%29%2B9%28%286%2F5%29%5E2-1%29-12%286%2F5-1%29
P%281200%29=-2%28216%2F125-125%2F125%29%2B9%2836%2F25-25%2F25%29-12%286%2F5-5%2F5%29
P%281200%29=-2%2891%2F125%29%2B9%2811%2F25%29-12%281%2F5%29
P%281200%29=%28-182%2F125%29%2B%2899%2F25%29-%2812%2F5%29
P%281200%29=%28-182%2F125%29%2B%28495%2F125%29-%28300%2F125%29
P%281200%29=%2813%2F125%29
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P=P%281200%29P%281200%29P%281200%29
P=%2813%2F125%29%5E3
highlight%28P=2197%2F1953125%29 or approximately,
P=0.00113