If a person after 10 steps is at his starting position, then this person takes 5 steps forward and 5 steps backward.
This is a binomial distribution with
- probability to take step forward [tex]p=0.6;[/tex]
- probability to take step backward [tex]q=0.4;[/tex]
- [tex]n=10.[/tex]
Then
[tex]Pr(\text{5 steps forward and 5 steps backward})=C_{10}^5p^5q^5=\\ \\=\dfrac{10!}{5!(10-5)!}\cdot (0.6)^5\cdot (0.4)^5=\dfrac{10!}{5!\cdot 5!}\cdot (0.6\cdot 0.4)^5=\\ \\=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10}{5!\cdot 2\cdot 3\cdot 4\cdot 5}\cdot (0.24)^5=7\cdot2\cdot 9\cdot 2\cdot (0.24)^5=252\cdot (0.24)^5=0.2006581248.[/tex]
Answer: [tex]252\cdot (0.24)^5=0.2006581248.[/tex]
