Grandma's Tweetin'

Siuan's grandmother recently signed up for a twitter account. She only follows five people - her five grandchildren. Each day, each of her grandchildren make two tweets and at the end of the day Siuan's grandmother gets an e-mail that lists all ten tweets in chronological order. If the times of each grandchild's tweets are random, the probability that no consecutive pair of tweets in the e-mail are by the same person can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

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