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A caretaker is giving candy to his two babies. Every minute, he gives a candy to one of his two babies at random. The five possible moods for the babies to be in, from saddest to happiest, are "upset," "sad," "okay," "happy," and "delighted." A baby gets happier by one mood when they get a candy and gets sadder by one mood when the other baby gets one. Both babies start at the "okay" state, and a baby will start crying if they don't get a candy when they're already "upset". The probability that 10 minutes pass without either baby crying can be expressed as

\frac{p}{q}

. Compute

p+q

.
2022 CCA Math Bonanza Team Round #7

T7

Problems(1)