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?
+23245 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
