Chapter 3, Problem 1UA

A “Daily Number” lottery has a three-digit number from 000 to 999. You buy one ticket each day. Your number is 389.

1. What is the probability of winning next Tuesday and Wednesday?

To determine

To find: The probability of winning the lottery next Tuesday and Wednesday.

Answer to Problem 1UA

The probability of winning the lottery next Tuesday and Wednesday is 0.000001.

Explanation of Solution

Given info:

A lottery has a three digit number from 000 to 999. Also, the number is 389.

Calculation:

Let event A denote the winning ticket on next Tuesday and B be denote that winning ticket on next Wednesday.

Here, the winning ticket on next Wednesday is not affected by winning ticket on next Tuesday. Thus, the selections are independent.

The formula for probability of event A is,

$P\left(A\right)=\frac{\text{Number of outcomes in event }A}{\text{Total number of outcomes in sample space}}$

Substitute 1 for ‘Number of outcomes in event A’ and 1,000 for ‘Total number of outcomes in sample space’,

$\begin{array}{c}P\left(A\right)=\frac{1}{1,000}\\ =0.001\end{array}$

The formula for probability of event B is,

$P\left(B\right)=\frac{\text{Number of outcomes in event }B}{\text{Total number of outcomes in sample space}}$

Substitute 1 for ‘Number of outcomes in event B’ and 1,000 for ‘Total number of outcomes in sample space’,

$\begin{array}{c}P\left(B\right)=\frac{1}{1,000}\\ =0.001\end{array}$

Multiplication rule for Independent Events:

If the events A and B are independent the probability of occurring of event B is does not affected by event A, that is $P\left(A\text{ and }B\right)$ becomes $P\left(A\right)\times P\left(B\right)$.

The required probability is,

$\begin{array}{c}P\left(A\text{ and }B\right)=P\left(A\right)\times P\left(B\right)\\ =0.001\times 0.001\\ =0.000001\end{array}$

Therefore, the probability of winning next Tuesday and Wednesday is 0.000001.

Interpretation:

There is a 0.000001 probability of winning next Tuesday and Wednesday.