##4.a
log(.5) / log(499 / 500)

##4.b
i <- 1
p <- 1
while (p > .5) {p <- p * (365 - i) / 365; i <- i + 1; print(c(1 - p, i))}

##4.c
i <- 1
p <- 1
while (p > .5) {p <- p * (200 - i) / 200; i <- i + 1; print(c(1 - p, i))}