Chapter 8.1, Problem 8.11E

(a)

To determine

To explain how you could use either table B or your calculator to stimulate thirty random birthdays from the $365$ possible days.

Explanation of Solution

  $\begin{array}{l}\text{Given: Bet \$1 that at least 2 of the students were born on the same day of the year}\text{.}\\ \text{By calculator,}\\ \text{let 1 to 365 represent the 365 days in a year}\text{.}\\ \text{You can carry out the stimulation for 30 students by using the following command}\\ \text{for a Ti-83/84 calculator:}\\ randInt(1,365,30)\end{array}$

(b)

To determine

To carry out stimulation and perform ten repetitions and explain should you take Austin’s bet.

Explanation of Solution

I will use the calculator command in part (a).

If all values in the result are different then you will win the bet. Else Austin will win the bet.

We carry out stimulation ten times and record who wins each time.

First stimulation: You win.

Second stimulation: you win.

And so on….

Sixth stimulation: Austin wins.

..

We note that we won $7\text{ out of 10}$ which is the majority of the number of games and thus we should take Austin’s bet.

(c)

To determine

To explain after combining results will we be surprised.

Explanation of Solution

Combine your results with the results of the other members of the class.

The result should be at about $30\%$ .

We then note that results in part (b) was very surprising because $7\text{ out of 10}$ corresponds with $70\%$ and this is much higher than $30\%$ .