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10/16 = .625

Analysis:

a and d will be odd if and only if both are odd. Therefor, ad will be odd 1/4 the time.

The same goes for bc. It will be odd 1/4 off the time.

ad-bc is even if and only if both ad and bc are either odd or even.

It's easiest to solve it from here with a table:

ad bc ad-bc prob

even even even 3/4*3/4 = 9/16

even odd odd 3/4*1/4 = 3/16

odd even odd 1/4*3/4 = 3/16

odd odd even 1/4*1/4 = 1/16

So, ad-bc will be even 9/16+1/16 = 10/16 of the time.

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โˆ™ 2010-05-01 17:25:03
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Q: Integers a b c and d not necessarily distinct are chosen independently and at random from 0 to 2007 inclusive What is the probability that ad-bc is even?
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