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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

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

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  • 2
    $\begingroup$ Did you try it ? $\endgroup$ – Qwerty Jun 19 '16 at 13:17
  • $\begingroup$ Tried but not able to solve $\endgroup$ – Gooner Jun 19 '16 at 14:10
  • $\begingroup$ Try to show your working and use proper punctuation marks in future.Thanks!!(from a review)... $\endgroup$ – tatan Jun 19 '16 at 14:55
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Hint:

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: $$\Pr(X<Y)=\int\Pr(X<y)dF_Y(y)$$

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  • $\begingroup$ Can you please elaborate $\endgroup$ – Gooner Jun 19 '16 at 14:10
  • $\begingroup$ 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. $\endgroup$ – drhab Jun 19 '16 at 17:01

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