hw2 problem 1 problem 2 problem 3 problem 4 problem 5 problem 6 (a) (b) (c) problem 7 problem 8

hw2

tags probability

2023PB_HW2.pdf

problem 1

412×38×28×24=1.56%\frac{4}{12}\times\frac{3}{8}\times \frac{2}{8}\times\frac{2}{4}=1.56\%

problem 2

1−c45×4!54=1−0.192=80.8%1-\frac{c_4^5\times 4!}{5^4}=1-0.192=80.8\%

problem 3

1−c448c452=1−0.718=28.1%1-\frac{c_4^{48}}{c_{4}^{52}}=1-0.718=28.1\%

problem 4

c811×8!118=3.1%\frac{c_{8}^{11}\times8!}{11^8}=3.1\%

problem 5

Evey level at least have one people leave so only 3 people can chose leave level freely

c36∗3(6−3)36=2033=74%\frac{c_{3}^{6}*3^{(6-3)}}{3^{6}}=\frac{20}{3^{3}}=74\%

problem 6

(a)

312=5314413^{12}=531441

(b)

12!6!×6!=924\frac{12!}{6!\times 6!}=924

(c)

12!3!×4!×5!=27720\frac{12!}{3!\times 4!\times 5!}=27720

problem 7

1−6!66=1−0.015=98%1-\frac{6!}{6^6}=1-0.015=98\%

problem 8

8!3!×3!×2!68=0.033%\frac{\frac{8!}{3!\times 3! \times 2!}}{6^8}=0.033\%