Chapter 14, Problem 43E

a)

To determine

To find the probability that the winning three numbers match the date on any given day.

Answer to Problem 43E

The probability that the winning three numbers match the date on any given day = 0.001

Explanation of Solution

There are 1000 three-digit number between 000-999.

Therefore,

  $P\left(threenumbersmatchdate\right)=\frac{1}{1000}=0.001$

b)

To determine

To find the probability that a whole year passes without this happening.

Answer to Problem 43E

The probability that a whole year passes without this happening = 0.694

Explanation of Solution

The probability that there are no matches for a whole year is,

  $\begin{array}{l}$ P\left(nomatchesforawholeyear\right)={(1-P(match))}^{365}$P\left(nomatchesforawholeyear\right)=0.694\end{array}$

c)

To determine

To find the probability that the date and winning lottery number match at least once during any year.

Answer to Problem 43E

The probability that the date and winning lottery number match at least once during any year = 0.306

Explanation of Solution

Calculation:

  $\begin{array}{l}P\left(match\text{ at least}\text{once}\right)=1-P(nomatchesallyear)\\ P\left(match\text{ at least}\text{once}\right)=1-0.694=0.306\end{array}$

d)

To determine

To find the probability that at least one of them will come up 9-1-1 on September 11.

Answer to Problem 43E

The probability that at least one of them will come up 9-1-1 on September 11 = 0.0488

Explanation of Solution

The probability that none of the 50 states draw (9-1-1) is,

  $\begin{array}{l}P\left(\text{we draw 9-1-1}\right)=1-P(don\text{'}tdraw9-1-1)\\ $ P\left(\text{we draw 9-1-1}\right)=1-{(0.999)}^{50}=0.0488$\end{array}$