Question 1106228
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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.<br>
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.<br>
6 of the 20 pairs satisfy the given condition; the probability is 6/20 = 3/10.