Answer
$P(at~most~27)=0.0217$
Since $P(at~most~27)=0.0217$ the expected value for 100 trials is $E(at~most~27)=100\times0.0217=2.17$. It is almost half of the results in d). For better results, we should use a larger number of samples (maybe 10,000).
Work Step by Step
$P(x)={}_nC_{x}~p^x~(1-p)^{n-x}$
$n=30$, $p=0.98$ and $1-p=0.02$
$P(at~least~28)=P(28)+P(29)+P(30)={}_{30}C_{28}\times0.98^{28}\times0.02^2+{}_{30}C_{29}\times0.98^{29}\times0.02^1+{}_{30}C_{30}\times0.98^{30}\times0.02^0=\frac{30!}{28!\times2!}\times0.98^{28}\times0.02^2+\frac{30!}{29!\times1!}\times0.98^{29}\times0.02+\frac{30!}{30!\times0!}\times0.98^{30}\times1=0.9783$
The probability that at most 27 of the 30 males survive to age 30 is the complement of the probabilty that at least 28 of the 30 males survive to age 30.
$P(at~most~27)=1-P(at~least~28)=1-0.9783=0.0217$
