Chapter 13.9, Problem 29PPS

i.

To determine

No. of PINs can you choose to lock cell phone.

Answer to Problem 29PPS

Total number of $4$ digit personal identification numbers that can be chosen to lock is $10000$ .

Explanation of Solution

Given:

Cell phone has a $4$ digit personal identification number (PIN) to lock it from use.

Concept Used:

For selecting the personal identification number order is important so arrangement is permuration.

Calculation:

As there are $10$ digits from $0$ to $9$ , so there are $10$ choices for the first place.

Since the digits can be repeated, there are $10$ choices for the third place as digits can be anyone from $0$ to $9$ .

For fourth place, so there are $10$ choices for the digit.

So $10\times 10\times 10\times 10=10000$ ways of selecting $4$ digit personal identification number.

Conclusion:

Therefore, total number of $4$ digit personal identification numbers that can be chosen to lock is $10000$ .

ii.

To determine

Probability to explain how someone is unlikely to guess your PIN.

Answer to Problem 29PPS

Probability how unlikely can someone guess the Pin is $\frac{9999}{10000}$ .

Explanation of Solution

Given:

Cell phone has a $4$ digit personal identification number (PIN) to lock it from use.

Concept Used:

For selecting the personal identification number order is important so arrangement is permutation.

Calculation:

Assume, probability how unlikely someone guesses the PIN is $P$ .

Probability how likely someone guesses the PIN is $R$ .

After that probability how unlikely someone guesses the PIN is equal to $1$ minus the probability how likely someone guesses the PIN.

i.e. $P-1=R$

As, there are $10000$ ways of choosing a PIN, the probability how likely someone guesses the PIN is $\frac{1}{10000}$ .

That is,

  $\begin{array}{l}R=\frac{1}{10000}\\ P=1-R\\ =1-\frac{1}{10000}\\ =\frac{10000-1}{10000}\\ =\frac{9999}{10000}\end{array}$

Conclusion:

Therefore, probability how unlikely can someone guess the Pin is $\frac{9999}{10000}$ .