“Hot spots” are species-rich geographical areas. A Nature (Sept. 1993) study estimated the probability of a bird species in Great Britain inhabiting a butterfly hot spot at .70. Consider a random sample of 4 British bird species selected from a total of 10 tagged species. Assume that 7 of the 10 tagged species inhabit a butterfly hot spot.
a. What is the probability that exactly half of the 4 bird species sampled inhabit a butterfly hot spot?
b. What is the probability that at least 1 of the 4 bird species sampled inhabits a butterfly hot spot?