Answer
a)0.009
b)0.38
c)0.97
d)3
Work Step by Step
Let $X$ be the random variable of number of updates. $X$ has the binomial distribution with parameters $n=10, p$, We can calculate the parameter $p$ directly from the table given in the exercise $3-34:$
$$
p=0.25+.05=0.3
$$
The probability mass function of $X$ is given by:
$$
\mathbb{P}(X=x)=\left(\begin{array}{l}
10 \\
x
\end{array}\right) 0.3^{x} \times(0.7)^{10-x}, x=0,1, \ldots, 10
$$
Calculate using this formula:
$$
\begin{array}{l}
\mathbb{P}(X=7)=0.009 \\
\mathbb{P}(X \leq 2)=\mathbb{P}(X=0)+\mathbb{P}(X=1)+\mathbb{P}(X=2)=0.38 \\
\mathbb{P}(X \geq 1)=1-\mathbb{P}(X=0)=0.97\\
\mathbb{E}(X )=np=0.3\times10=3
\end{array}
$$
