SOLUTION: David chooses numbers from two hats, one red and one blue. The red hat contains all even digits greater than zero, and the blue hat contains all odd digits greater than zero. The
Algebra ->
Permutations
-> SOLUTION: David chooses numbers from two hats, one red and one blue. The red hat contains all even digits greater than zero, and the blue hat contains all odd digits greater than zero. The
Log On
Question 1106228: David chooses numbers from two hats, one red and one blue. The red hat contains all even digits greater than zero, and the blue hat contains all odd digits greater than zero. The numbers picked are used to form fractions. The red number is the numerator, and the blue number is the denominator. What is the probability that David’s fraction will greater than 1/2 but less than 1? Answer by greenestamps(13200) (Show Source):
There are 4 even digits in the red hat and 5 odd digits in the blue hat. If one digit is chosen from each hat, the number of pairs of digits is 4*5=20.
To find which pairs form fractions with a value greater than 1/2 and less than 1, simply list them. They are
2/3; 4/5 and 4/7; 6/7 and 6/9; and 8/9.
6 of the 20 pairs satisfy the given condition; the probability is 6/20 = 3/10.
