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Edexcel S2 June 2010 Q3 need some help!

This question is getting on my nerves.

I got P(X>6) = 1/6 but why do you have to work out P(X<4)= 1/2 and add the answers together. I think the answer is 2/3.

So yeah can anyone explain this question to me in DETAIL, it would be much appreciated
JUne 2010(2).pdf201.7KB
Reply 1
Avatar for jackandjill
jackandjill
i'm having the exact same problem as you, i just don't get it! where do you get the P(X < 4) from? why the 4?
Reply 2
Avatar for Gibbo81
Gibbo81
1
Here is the question

A rectangle has a perimeter of 20 cm. The length, X cm, of one side of this rectangle is
uniformly distributed between 1 cm and 7 cm.
Find the probability that the length of the longer side of the rectangle is more than 6 cm
long.

Now you have calculated the Prob that X is longer than 6 which is what the question asked you to do. Try drawing a rectangle with the horizontal sides 6cm long, the other sides will have to be 4cm to make a total perimeter of 20cm as specified in the question 6+4+6+4=20. Obviously if X is bigger than 6 then the other sides of the rectangle will be smaller than 6.

What you have not considered is if X is in fact the shortest side of the rectangle. In that case the other sides of the rectangle would be bigger than 6cm. Again draw a rectangle where the horizontal sides are 4cm if the perimeter has to be 20 then the other two sides (the vertical ones) will be 6. Now if X<4 then the other two sides must be bigger than 6.

That's where the other probability comes from.

Hope that's clearer!
(edited 12 years ago)

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