Q 28. Lotto In the United Kingdom鈥檚 ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 5: Q 28. (page 297)

Lotto In the United Kingdom鈥檚 Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought one ticket for herself and one for each of her four adult children. She had the lottery computer randomly select the six numbers on each ticket. When the six winning numbers were drawn, Rosemary was surprised to find that none of these numbers appeared on any of the five Lotto tickets she had bought. Should she be? Design and carry
out a simulation to answer this question. Follow the four-step process.

Short Answer

Expert verified

As a consequence, $4$ or all $5$ simulations share a common number.

Step by step solution

Step 1. Given Information

Use numbers with two digits. The numerals $00$ through $02$ can be used to represent $b i n g o$ . The numbers between $03$ and $99$ should be used to signal $n o b i n g o$ . Count the required number of $2$ -digit numbers until $b i n g o$ is obtained.

Step 2. Concept Used

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$ (never happens) and $1$ (happens frequently) (always occurs).

Step 3. Explanation

Use two-digit numbers instead of three-digit numbers. Let the numbers $01$ to 4 $49$ represent the ticket's matching number. Ignore the numerals $50$ through $99$ , as well as the number $00$ . Six numbers, ranging from $01$ to $49$ , are drawn at random, with no repeats. Repeat this simulation six times and count how many simulations (except the first) have the same number as the first. You'll almost certainly get a result that says $4$ or $5$ simulations all have the same number.