TDSM 5.7

a. (1-47.1%)*(1-47.1%)*47.1%=0.1318051

b. 47.1%*47.1%*47.1%=0.1044871

c. According to geometric distribution,

      p=47.1%
      
      μ=1/p=2.123142

      Variance=(1-p)/p*p=2.38459077, so standard deviation=1.544212

d. p=30%

      μ=1/p=3.3333

      Variance=(1-p)/p*p=7.77777778, so standard deviation=2.788867

e. As we can see from (c) and (d), there is an inverse relationship between the probability and the expected wait time until success (or mean). This makes intuitive sense: the less likely something is to be a success, the longer you have to wait, or the more trials that will be necessary before success.