Fibonacci Sequence Study

The Fibonacci sequence begins like this: 1, 1, 2 , 3, 5, 8 , 13, 21, 34

1/3 of the numbers in the Fibonacci sequence are even, because an odd number plus an odd number is even, and an odd number plus an even number is odd.

To achieve an even number when multiplying two numbers, either or both numbers must be even.

You can therefore think of the problem as asking, "What is the probability that I will NOT choose two odd numbers?" The probability you WILL choose two odd numbers is ( $\frac{2}{3}$ )( $\frac{2}{3}$ )= $\frac{4}{9}$ .

The probability that the two numbers will NOT both be odd is 1- $\frac{4}{9}$ = $\boxed {\frac{5}{9}}$