Question

A bag contains one chip labeled "1," two chips labeled "2," three chips labeled "3," and so on, all the way up to 100 chips being labeled "100." if one chip is randomly chosen, then what is the chance that it has an even number less than or equal to 50?

Answer 1

Answer:

13 / 101

Step-by-step explanation:

# chips = 1 + 2 + 3 + ... + 100 = 100 × 101 / 2 = 50 × 101

# chips with even number less than or equal to 50

 = 2 + 4 + 6 + ... + 50

 = 2 × ( 1 + 2 + 3 + ... + 25 )

 = 2 × 25 × 26 / 2

 = 25 × 26

 = 50 × 13

P( getting an even number less than or equal to 50 )

 = ( # chips with even numbers less than or equal to 50 ) / ( # chips )

 = ( 50 × 13 ) / ( 50 × 101 )

 = 13 / 101