# What are the odds that truck a arrives before truck b? [closed]

given truck a arrives at a random time between 9am and 11am, and truck b arrives at a random time between 10am and 12pm (noon). what are the odds that truck a arrives before truck b

## closed as off-topic by choco_addicted, gebruiker, Shailesh, Daniel W. Farlow, timurJun 19 '16 at 15:22

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• Did you try it ? – Qwerty Jun 19 '16 at 13:17
• Tried but not able to solve – Gooner Jun 19 '16 at 14:10
• Try to show your working and use proper punctuation marks in future.Thanks!!(from a review)... – tatan Jun 19 '16 at 14:55

If $X,Y$ are two random variables on the same probability space then:$$\Pr(X<Y)=\int\Pr(X<Y\mid Y=y)dF_Y(y)=\int\Pr(X<y\mid Y=y)dF_Y(y)$$
If moreover $X$ and $Y$ are independent then: $$\Pr(X<y\mid Y=y)=\Pr(X<y)$$ so that: $$\Pr(X<Y)=\int\Pr(X<y)dF_Y(y)$$
• Let $X$ be the arrival time of truck a and let $Y$ be the arrival time of truck b. The distributions of $X$ and $Y$ are well known then (uniform on interval $(9,11)$ and uniform on interval $(10,12)$ respectively). So you have all ingredients necessary to apply the hint, and should at least make an effort. If you don't succeed then you can ask a new question, explaining what you tried and where you got stuck. – drhab Jun 19 '16 at 17:01