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A hat contians one chip marked with the number 1, two chips marked with the number 2, and so on, through one hundred chips marked with the number 100.  You draw a chip at random.  What is the probability that the chip has an even number?

 May 11, 2020
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Both of these series will be arithmetic. The formula for the sum of an arithmetic series is:  Sum  =  n(f + l) / 2

where:  n  =  number of numbers     f  =  first number     l  =  last number

 

There are 100 chips, 50 will be even and 50 will be odd.

Total number of chips:  Sum  =  100(1 + 100) / 2  =  5050

 

Odd numbered chips:  1 + 3 + 5 + 7 + ... + 99  =  50(1 + 99) / 2  =  2500

 

Even numbered chips:  2 + 4 + 6 + 8 + ... + 100  =  50(2 + 100) / 2  =  2550

 

The probability that the chip will have an even number  =  2550 / 5050

 May 11, 2020

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