Mrs. Wheeler prepares a list of 434343 US presidents, 313131 of whom served in the military. Then 888 students each select a president at random (there can be repeats) for their civics presentations.What is the probability that at least one of the students will select a president who did not serve in the military?

Answer: Probability of atleast one of the students(888) selecting a president with no service in the military reaches 1. Step-by-step explanation: Total Presidents in list = 434343 Military men to be president = 313131 Probability of selecting President who were also military men = p = 313131/434343 = 0.72 Probability of selecting President who were not military men = q = 1 - p = 1 - 0.72 = 0.28 Now; no of students who make a choice = 888 no. of Choices made resulting in success = x : {0, 1, 2, 3,............., 888 } GIVEN CASE:P(f) = Probability of atleast one student selecting a president with no service in military This case fails when no one selects a president with no service in military, let us call it P(f').P(f) = 1-P(f')Calculating P(f'):Let us define:Failure = selecting a president with service in military , p = 0.72Success = selecting a president with no service in military , q = 0.28Using Binomial Theorem:we have this case when n students make selections and x of them are successful. [tex]P(x) = nCx * q^{x}  * p^{n-x}[/tex]In case of f' , n = 888 and x = 0[tex]P(0) = 888 C 0 * (0.28)^{0}  * 0.72^{888-0}[/tex][tex]= (888!/(888-0)!) * (1) * (0.72)^{888}\\= (0.72)^{888}\\= 2.047655e-127\\[/tex]Hence, P(f') = 2.047655e-127 (reaches 0)Now: P(f) = 1 - P(f')P(f) = 1 - 2.047655e-127 = 1Hence Probability of atleast one of the students(888) selecting a president with no service in the military is 1.