Wilbur and Doris are two Boston Terrier puppies who have recently started dating. Doris and Wilbur met up at the beach yesterday and their doggy parents supplied them with an infinite number of stuffed animal toys to play with. The two dogs speak each other's language, of course, and they seemingly agreed to play a game where they each race to bury a total of 10 toys each, one after the other, in the sand. Naturally, the first to do so wins. Sadly, Wilbur only successfully buries each toy he grabs with probability 0.7, because a mean seagull often grabs his toy before he can bury it. Almost as sad is that Doris only successfully buries each toy she grabs with probability 0.8, because a jealous sand crab occasionally scurries to grab her toy before she can bury it. If you needed one more reason explaining why dating is so difficult, you have one. The number of toys Wilbur must grab before ultimately burying 10 of them is guided by a Negative Binomial with parameters r=10 and p=0.7. Similarly, the number of toys that Doris needs to grab before ultimately burying ten of them is also a Negative Binomial with parameters r=10 and p=0.8. Restated, if we let W and D be independent random variables counting the number of toys that Wilbur and Doris try to bury, respectively, then: W∼NegBin(r=10,p=0.7)D∼NegBin(r=10,p=0.8)​ Next Question: Next Question:  What's the probability that, between the two of them, they grab at most 25 toys? Present your answer out to three decimal places.

Wilbur and Doris are two Boston Terrier puppies who have recently started dating. Doris and Wilbur met up at the beach yesterday and their doggy parents supplied them with an infinite number of stuffed animal toys to play with. The two dogs speak each other's language, of course, and they seemingly agreed to play a game where they each race to bury a total of 10 toys each, one after the other, in the sand. Naturally, the first to do so wins.

Sadly, Wilbur only successfully buries each toy he grabs with probability 0.7, because a mean seagull often grabs his toy before he can bury it. Almost as sad is that Doris only successfully buries each toy she grabs with probability 0.8, because a jealous sand crab occasionally scurries to grab her toy before she can bury it.

If you needed one more reason explaining why dating is so difficult, you have one.

The number of toys Wilbur must grab before ultimately burying 10 of them is guided by a Negative Binomial with parameters r=10 and p=0.7. Similarly, the number of toys that Doris needs to grab before ultimately burying ten of them is also a Negative Binomial with parameters r=10 and p=0.8. Restated, if we let W and D be independent random variables counting the number of toys that Wilbur and Doris try to bury, respectively, then:

Next Question: Next Question:  What's the probability that, between the two of them, they grab at most 25 toys? Present your answer out to three decimal places.