Step 1 :Given that the blood type O negative is the universal donor type and is crucial to blood banks. However, this blood type is fairly rare with only 5% of U.S. residents having type O negative blood. Assume that a blood bank has recruited 18 donors.
Step 2 :We are asked to find the probability that two or more of them have type O negative blood. The probability is found to be 0.2265.
Step 3 :We are also asked to find the probability that fewer than four of them have type O negative blood. To find this, we use the binomial probability formula which is given by \(P = C \times (p^k) \times ((1 - p)^{n - k})\), where \(C\) is the number of combinations of \(n\) items taken \(k\) at a time, \(p\) is the probability of success on each trial, and \(k\) is the number of successes.
Step 4 :In this case, the number of trials \(n\) is 18 (the number of donors), the probability of success on each trial \(p\) is 0.05 (the probability that a randomly chosen person has type O negative blood).
Step 5 :We calculate the total probability of fewer than four donors having type O negative blood by summing up the binomial probabilities for \(k = 0, 1, 2, 3\).
Step 6 :The total probability is found to be 0.9891267763910727.
Step 7 :Rounding to four decimal places, the final answer is \(\boxed{0.9891}\).