1. The Vancouver Island marmot (Marmota ancouverensis) is a species of marmot that is naturally found...

 

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1. The Vancouver Island marmot (Marmota ancouverensis) is a species of marmot that is naturally found in the mountainous regions of Vancouver Island, The specles faced near extinction in the 1990 when dangerously low observed wild population numbers prompted human intervention. From this, a breeding program was established with locations in Toronto, Calgary, and Langley. Though the species still remains classified as critically endangered, these breeding programs helped bring the wild population numbers from less than 30 in 2003 to an estimated 250-300 in 2013. Suppose that 30% of female marmots in the breeding program give birth to a litter of exactly 3 pups. A collection of 20 female marmots from the breeding program who recently gave birth to a litter is selected independently and at random, and the number of litters with exactly 3 pups is recorded, (a) [1 mark] What is the expected number of these litters that were NOT exactly 3 pups? (b) [1 mark) What is the probability that from these litters, exactly 7 of the litters contained exactly 3 pups? (c) [1 mark] What is the probability that from these litters, at least 6 of them contained exactly 3 pups? (d) [2 marks] If it is known that at least 4 of the litters had exactly 3 pups, what is the probability that exactly 5 of the litters had exactly 3 pups? 1. The Vancouver Island marmot (Marmota ancouverensis) is a species of marmot that is naturally found in the mountainous regions of Vancouver Island, The specles faced near extinction in the 1990 when dangerously low observed wild population numbers prompted human intervention. From this, a breeding program was established with locations in Toronto, Calgary, and Langley. Though the species still remains classified as critically endangered, these breeding programs helped bring the wild population numbers from less than 30 in 2003 to an estimated 250-300 in 2013. Suppose that 30% of female marmots in the breeding program give birth to a litter of exactly 3 pups. A collection of 20 female marmots from the breeding program who recently gave birth to a litter is selected independently and at random, and the number of litters with exactly 3 pups is recorded, (a) [1 mark] What is the expected number of these litters that were NOT exactly 3 pups? (b) [1 mark) What is the probability that from these litters, exactly 7 of the litters contained exactly 3 pups? (c) [1 mark] What is the probability that from these litters, at least 6 of them contained exactly 3 pups? (d) [2 marks] If it is known that at least 4 of the litters had exactly 3 pups, what is the probability that exactly 5 of the litters had exactly 3 pups?

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