The Vancouver Island mannot {Manners vancouverensis] is a species of man'nct that is naturally found in the mountainous regions of Vancouver Island. The species faced near extinction in the 1990s 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 classied as critically endangered. these breeding programs helped bring the wild population numbers from less than 30 in 21.113 to an estimated 250-301} in 2013. Suppose that 40% of female marmcts in the breeding program give birth to a litter of exactly 1 pup. A collection of 15 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 1 pup is recorded. {a} [1 mark] What is the expected number of these litters that were NOT exactly 1 pup? Suppose that 40% of female marmots in the breeding program give birth to a litter of exactly 1 pup. A collection of 15 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 1 pup is recorded. (b) [2 marks] What is the probability that from these litters, exactly 7 of the litters contained exactly 1 pup?Suppose that d% of female marmots in the breeding program give birth to a litter of exactly 1 pup. A collection of 15 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 1 pup is recorded. {c} [2 marks] What is the probability that from these litters. at least 5 of them contained exactly 1 pup? Suppose that 40% of female marmots in the breeding program give birth to a litter of exactly 1 pup. A collection of 15 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 1 pup is recorded. [d] [2 marks] If it is known that at least 4 of the litters had exactly 1 pup, what is the probability that exactly 6 of the litters had exactly 1 pup