Chapter 13.9, Problem 12PPS

To determine

To calculate: Probability that a randomly selected phone number with these digits will be her friends.

Answer to Problem 12PPS

Probability that a randomly selected phone number with these digits will be her friends is $\frac{1}{6}$ .

Explanation of Solution

Given information:

Ivy knows that the last four digits of her friend’s phone number contain the digits $0,3,5,6$ .

Calculation:

At the time of choosing phone number, order is important.

So permutation is used.

As the first digit of her friends phone number is $5$ .

There are $3$ choices for the second digit.

  $2$ choices for the third digit,

  $1$ choices for the fourth digit.

Thus,

  $\begin{array}{l}P\left(3,1\right)=\mathrm{3.2.1}\\ =6\end{array}$

Thus, total number of ways is $6$ .

Selecting the phone number is unique, therefore the favourable number of cases is only $1$ .

For calculating probability that the randomly selected phone number with these digits will be her friends.

Probability,

  $\begin{array}{l}=\frac{favourablenumberofcases}{Totalnumberofcases}\\ =\frac{1}{6}\end{array}$