Willy is a Dumby

Discrete Mathematics Level 4

Mr. Siddique asks his 1st grade class (containing Willy and David) to create a six-digit string of 0's and 1's such that there is at least one string of two consecutive 1's. For example, the numbers \[111110\] and \[010110\] fulfill this requirement, however, \[010101\] does not.

However, though their task isn't too hard, Willy and David are dumbies, so they randomly write six 0's or 1's.

Mr. Siddique will be very mad if neither Willy nor David completes this simple task, and will retire from his teaching job and travel to Bangladesh to see one of the greatest countries in the world. However, this is bad because Willy and David love Mr. Siddique and if he leaves, Willy and David will cry.

What is the probability that Willy and David will cry because Mr. Siddique leaves to go to Bangladesh?

The answer can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are positive integers and are relatively prime to each other. Find the sum \(a+b\).


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