## how mant random matrices

Professor Johnson is interested in the probability that a certain type of ran-
domly generated matrix has a positive determinant. His student attempts to calculate
the probability exactly, but runs into difficulty because the problem requires her to
evaluate an integral in 9 dimensions. Professor Johnson therefore decides to obtain an
approximate probability by simulation, i.e., by randomly generating some matrices and
observing the proportion that have positive determinants. His preliminary investiga-
tion reveals that the probability is roughly 0.05. At this point, Professor Park decides
to undertake a more comprehensive simulation experiment that will, with 0.95-level
confidence, correctly determine the probability of interest to within ±0.00001. How
many random matrices should he generate to achieve the desired accuracy?