Chapter 8, Problem 8.68RE

(a)

To determine

To calculate how many digits were $1,2\text{ or 3}$ and also calculate what is the approximate probability the first of the four individual digits in a telephone number is $1,2\text{ or 3}$ .

Answer to Problem 8.68RE

The estimated probability is thus $0.31$ .

Explanation of Solution

Randomly select a page in your local telephone directory. Record the last four digits of the first hundred telephone numbers.

A possible result is:

  $1274,9436,1875,\mathrm{..},3482$

In total we have:

  $4\times 100=400\text{ digits}\text{.}$

In the sample:

  $124\text{ of the 400 digits are a 1,2 or 3}\text{.}$

The probability is the number of favorable outcomes divided by the number of possible outcomes:

  $\begin{array}{l}P(\text{win)=}\frac{\text{favorable outcomes}}{\text{possible outcomes}}\\ =\frac{124}{400}\\ =\frac{31}{100}\\ =0.31\end{array}$

The estimated probability is thus $0.31$ .

(b)

To determine

To calculate what is the probability of getting $1,2\text{ or 3}$ and explain do you think first of the four individual digits in telephone numbers is equally likely to be any of the ten possible digits.

Answer to Problem 8.68RE

The theoretical probability is thus $0.3$ .

Explanation of Solution

  $1,2\text{ or 3 represents 3 of the 10 digits}\text{.}$

The probability is the number of favorable outcomes divided by the number of possible outcomes:

  $\begin{array}{l}P(\text{win)=}\frac{\text{favorable outcomes}}{\text{possible outcomes}}\\ =\frac{3}{10}\\ =0.3\end{array}$

The theoretical probability is thus $0.3$ .

It appears to be equally likely to obtain any of the ten possible digits because the estimated probability of $0.31$ is very close to the theoretical probability of $0.3$ .