*6. After a long wait, the Newborns were rewarded with quintuplets, two boys and three girls, thanks...

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*6. After a long wait, the Newborns were rewarded with quintuplets, two boys and three girls, thanks to the wonders of new medical advances. During the first 5 months, the babies' life consisted of two states: awake (and mostly crying) and asleep. According to the Newborns, the babies "awake-asleep" activities never coincide. Instead, the whole affair is totally random.

In fact, Mrs. Newborn, a statistician by profession, believes that the length of time each baby cries is exponential, with a mean of 30 minutes. The amount of sleep each baby gets also happens to be exponential, with a mean of 2 hours. Determine the following:

(a) The average number of babies who are awake at anyone time.

(b) TIle probability that all babies are asleep.

(c) The probability that the Newborns will not be happy because more babies are awake

(and crying) than are asleep.

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