Final answer:
This High School Mathematics question requires us to calculate the probabilities of certain numbers of smokers starting before 21 years of age using binomial probability, considering that 60% of smokers begin before this age and a sample of 10 smokers is selected.
Step-by-step explanation:
The question requires us to calculate the probability of certain outcomes when selecting 10 smokers who are 21 years old or older, given that 60% of adult smokers started smoking before 21 years old.
This is a binomial probability problem because we have a fixed number of trials (10 smokers), two possible outcomes for each trial (started smoking before 21 or not), and the probability of success (starting smoking before 21) remains constant (60% or 0.6).
Step-by-step calculation:
Calculate the probability that at least 8 out of 10 smokers started smoking before 21: To find this, we sum the probabilities of exactly 8, exactly 9, and exactly 10 smokers starting before 21.
Calculate the probability that at most 5 out of 10 smokers started smoking before 21: This includes summing probabilities of exactly 0 through exactly 5 smokers starting before 21.
Calculate the probability that exactly 2 out of 10 smokers started smoking before 21: This requires using the binomial probability formula for exactly 2 successes.
Without calculation, exact probabilities cannot be provided as they require statistical techniques or a calculator to compute the binomial probabilities based on the given success rate.