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Math 170(J. Wu) Answers to Homeworks
Homework 3:

page 143

5. (see the book)

6.

\begin{displaymath}
F\cap G=\{(t,t,t)\}.\end{displaymath}

\begin{displaymath}
P(F\cap G)=1/8.\end{displaymath}

19. (see the book)

20.

\begin{displaymath}
P(G\cap H)=4/36=1/9.\end{displaymath}

\begin{displaymath}
P(G\cup H)=20/36=5/9.\end{displaymath}

Page 153

4. $2\cdot 4\cdot 2=16$.

10.

\begin{displaymath}
{}_{10}P_6=10\cdot 9\cdot 8 \cdot 7\cdot 6\cdot 5=151200.\end{displaymath}

14.

\begin{displaymath}
{}_{10}C_6=\frac{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5}{6\cd...
 ... 1}=\frac{10\cdot 9\cdot 8\cdot 7}{4\cdot 3\cdot 2\cdot 1}=210.\end{displaymath}

24.

\begin{displaymath}
5!=5\cdot 4\cdot 3\cdot 2\cdot 1=120.\end{displaymath}

Page 164

22.

35/40=7/8.

24.

23/40.

Page 173

6.

\begin{displaymath}
\frac{1}{4}\cdot\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{4^3}=\frac{1}{64}.\end{displaymath}

28.

(a)
366 days; 4 years.
(b)

\begin{displaymath}
\frac{28\times 3+29}{365\times 3+366}=\frac{113}{1461}.\end{displaymath}

(c)

\begin{displaymath}
\frac{12\times 4}{365\times 3+366}=\frac{48}{1461}.\end{displaymath}

(d)

\begin{displaymath}
\frac{4}{365\times 3+366}=\frac{4}{1461}.\end{displaymath}

(e)

\begin{displaymath}
\frac{11\times 3+12}{365\times 3+366}=\frac{45}{1461}.\end{displaymath}

(f)

\begin{displaymath}
\frac{1}{365\times 3+366}=\frac{1}{1461}.\end{displaymath}

(g)
No.
(h)
No.
(i)
No.
(j)
(c) and (e); (c) and (f); (d) and (e); (d) and (f).

30.
\begin{diagram}
{}_{10}C_7(\frac{1}{4})^7(1-\frac{1}{4})^3+{}_{10}C_8(\frac{1}{4...
 ...^{10}}\\ =\frac{3676}{4^{10}}=\frac{919}{4^9}=\frac{919}{262144}\\ \end{diagram}


 

Jie Wu
11/13/1997