What's the difference between the following problems:
a) 40% of business travelers carry either a cell phone or a laptop computer (USA Today, September 12, 2000). For a sample of 15 business travelers, compute the probability that 3 of the travelers carry a cell phone or a laptop.
b) Through the week ending September 16, 2001, Tiger Woods was the leading money winner on the PGA Tour, with total earnings of $5,517,777. Of the top 10 money winners, 7 players used a Titleist brand golf ball (www.pgatour.com). Suppose that we randomly select 2 of the top 10 money winners. What is the probability that exactly one uses a Titleist golf ball?
In principle, not too much. However, in problem the first problem you are not given the population size but are, instead, given the probability of 'success' as 0.4 (So what is a success here?) You can therefore rightfully assume that the population is large enough that that probability does not change. In the second problem, the population is much smaller....and hence the probability changes each time a player is 'selected', i.e. for each successive event. So, the sampling distribution is different in each case....binomial for the first, hypergeometric for the second. So what are the solutions to the problems above?