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?

please help me to sove this problem