Question

Free-throw practice At the end of basketball practice, each player on the team must shoot free throws until he makes $10$of them. Dwayne is a $70\%$free-throw shooter. That is, his probability of making any free throw is $0.70$. We want to design a simulation to estimate the probability that Dwayne make$10$ free throws in at most $12$shots. Describe how you would use each of the following chance devices to perform one trial of the simulation.

a. Slips of paper

b. Random digits table

c. Random number generator

Short answer

a. The papers are then placed on a table, numbers facing down. Then jumble the sheets so you can't tell which number is on which table. And choose one of the paper slips. The free throw was made if the number was $1,2,3,4,5,6$or $7$; otherwise, the free throw was missed.

b. We'll now pick a row from the random digits database. After that, choose the first digits table. After that, choose the first digit. The free throw was made if the digit was between $1$and $7$(inclusive); otherwise, the free shot was missed.

c. we'll count how many numbers we need till we have ten digits ranging from $1$to $7$, indicating that $10$free shots were made.

Step-by-step solution

Part (a) Step 1 : Given Information

We have to describe how you would use slips of paper device to perform one trial of the simulation.

Part (a) Step 2 : Simplification

There is a basketball practice for each player to shoot free throws in the question, and there is a $0,70$chance of making any free throw, which equates to around $7$out of every $10$shots. As,

$$\begin{gathered} 0.70=\frac{70}{100} \\ =\frac{7}{10} \end{gathered}$$

Now we'll write the numbers $1$to $10$on separate slips of paper. After that,

$1,2,3,4,5,6,7$=Make free throw

$8,9,10$ = Miss free throw
The papers are then placed on a table, numbers facing down. Then jumble the sheets so you can't tell which number is on which table. And choose one of the paper slips. The free throw was made if the number was $1,2,3,4,5,6$or $7$; otherwise, the free throw was missed.

Now we'll continue until ten free throws have been made, and then we'll count how many trials it took to get ten free throws.

Part (b) Step 1 : Given Information

We have to describe how you would use random digit table device to perform one trial of the simulation.

Part (b) Step 2 : Simplification

There is a basketball practice for each player to shoot free throws in the question, and there is a $0.70$chance of making any free throw, which equates to around $7$out of every $10$shots. As,

$$\begin{gathered} 0.70=\frac{70}{100} \\ =\frac{7}{10} \end{gathered}$$

We'll now pick a row from the random digits database. After that, choose the first digits table. After that, choose the first digit. The free throw was made if the digit was between $1$and $7$(inclusive); otherwise, the free shot was missed. So, we'll keep going until we get ten free throws, then count how many trials it took to get ten free throws.

Part (c) Step 1 : Given Information

We have to describe how you would use random number generator device to perform one trial of the simulation.

Part (c) Step 2 : Simplification

There is a basketball practice for each player to shoot free throws in the question, and there is a $0.70$chance of making any free throw, which equates to around $7$out of every $10$shots.

As,

$$\begin{gathered} 0.70=\frac{70}{100} \\ =\frac{7}{10} \end{gathered}$$

Now we'll look at numbers one through ten, as follows:
Make a free throw with$1,2,3,4,5,6,7.$

Missed free throws $8,9,10$

Now, in your $Ti83/Ti84$calculator, type the following command, which will simulate $30$shots as:

$randInt(1,10,30)$, where$randInt$is located under PRB in the MATH menu.

As a result, we'll count how many numbers we need till we have ten digits ranging from $1$to $7$, indicating that $10$free shots were made.