Chapter 8.3, Problem 8.58E

(a)

To determine

To draw a Galton’s board with two or more rows of pegs and calculate the probability that a ball lands in Slot C.

Answer to Problem 8.58E

  $0.109375$ .

Explanation of Solution

The Galton’s board is as:

  

We note that:

  $\begin{array}{l}n=8\\ p=0.5\end{array}$

The ball ends up in Slot C, if the ball moved to the right of the peg two times and the ball moved to the left of the peg six times.

Evaluate at $k=2$ :

  $\begin{array}{l}$ P(X=2)=C{}_2\times {(0.5)}^2\times {(1-0.5)}^{8-2}$=28\times {0.5}^8\\ =0.109375\end{array}$

(b)

To determine

To calculate the probability that a ball lands in Slot F.

Answer to Problem 8.58E

  $0.21875$ .

Explanation of Solution

We note that:

  $\begin{array}{l}n=8\\ p=0.5\end{array}$

The ball ends up in Slot F, if the ball moved to the right of the peg five times and the ball moved to the left of the peg three times.

Evaluate at $k=5$ :

  $\begin{array}{l}$ P(X=5)=C{}_5\times {(0.5)}^5\times {(1-0.5)}^{8-5}$=56\times {0.5}^8\\ =0.21875\end{array}$